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WST
PUBUCATIONS
BUILDING SCIENCE SERIES
39
Use of Computers
for Environmental
Epgineering Related
to Buildings
DATE DUE
AUG 7
DEC % 1
CAVLORO
PRINTED IN U.S.A.
ATIONAL BUREAU OF STANOAI^S
FEB 1 6
1B3J.48
, u
C. ■So
UNITED STATES DEPARTMENT OF COMMERCE . Maurice H. Stans, Secretary
NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director
Use of Computers for Environmental
Engineering Related To Buildings
Proceedings of a Symposium Sponsored by the National Bureau
of Standards, the American Society of Heating, Refrigerating
and Air-Conditioning Engineers, Inc., and the Automated
Procedures for Engineering Consultants, Inc.
Held at the National Bureau of Standards
Gaithersburg, Maryland
November 30 - December 2.
Edited by
T. Kusuda
Institute for Applied Technology
National Bureau of Standards
Washington, D.C.
Building Science Series 39
Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 39, 826 pages (Sept. )
CODEN: BSSNB
Issued October
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.
(Order by SD Catalog No. C 13.29/2:39). Price $7. 75
Stock Number -
Abstract
These proceedings of the First Symposium on the Use of Computers for Environmental Engineering
Related to Buildings contain all of the technical papers and invited addresses presented at the
symposium, which was held November 30 - December 2, , at the National Bureau of Standards.
The fifty-nine papers deal with the application of the computer to such environmental engineer-
ing problems as building heat transfer calculations, heating and cooling load calculations, system
simulations, energy usage analyses, computer graphics, air and smoke movement inside buildings, and
weather data analyses for load and energy usage calculations.
Key Words: Building heat transfer analysis, energy usage, environmental engineering,
heating and air conditioning, use of computers
Library of Congress Catalog Card Number: 70 -
II
Foreword
For a number of years the National Bureau of Standards has been a leader in the development and
use of computers in scientific and engineering fields. We strongly believe that the effective applica-
tion of computers to the problems of the building industry will be of significant benefit to that in-
dustry. In what we hope to be a helpful step in this direction, we were pleased to be able to join
with the American Society of Heating, Refrigerating, and Air Conditioning Engineers and the Automated
Procedures for Engineering Consultants, Incorporated, in sponsoring this First Symposium on the Use
of Computers for Environmental Engineering Related to Buildings.
In recent years the use of computers has had a rapidly increasing impact on the design, performance
analysis, and control of environmental systems related to buildings. The purpose of the Symposium was
to provide a forum for exchange of the latest information and ideas among engineers, architects, and
planners who use computers. The Symposium attracted leading authorities in the field of environmental
engineering not only from all parts of the United States but also from many parts of the world. Over
400 architects and engineers representing the building industry, governments, universities, and utili-
ties participated. Applications of computer programs and calculation methods covering several topics
in environmental engineering are presented in these proceedings in a form useful to consulting firms,
government agencies, research organizations, and industrial firms.
Lewis M. Branscomb, Director
National Bureau of Standards
III
Preface
The use of computers is now widespread among environmental engineers working with buildings. Sub-
jects ranging from routine heating and cooling load calculations to sophisticated computer graphic dis-
play systems are being handled. Although the environmental engineers have been slow in adapting the
computer to their needs, at least until the middle of the 's, their use of the computer is now in-
creasing rapidly. This development is In fact taking place so fast that no major coordinated activities
for exchanging ideas and disseminating information have been undertaken except those of the APEC (Auto-
mated Procedures for Engineering Consultants). While the APEC is active mainly In the area of programs
for practicing engineers, needs are also recognized for advanced techniques or new procedures--such as
the calculation of accurate room temperature change under realistic climatic conditions, simulation of
air conditioning system d5mamics, optimization of the system and component selection based upcn rela-
tively advanced mathematical concepts, and effective use of graphic displays or data structuring. The
First Symposium on the Use of Computers for Environmental Engineering Related to Buildings was to serve
this need by providing opportunities for creative environmental engineers to meet each other and exchange
new ideas. Because this was the first symposixjm of its kind and because heating and cooling load cal-
culations are currently the most popular subject among the environmental engineers, the largest per-
centage of the papers presented dealt with the temperature and the thermal load calculations for
buildings. The papers presented illustrated that there exists much duplication of effort in many parts
of the world as well as In the United States. Although the program committee's selection of papers led
to some redundancy, the purpose of their inclusion was to encourage the participation of as many of the
first line investigators in the field who have been active in the use of computers for environmental
calculations. The symposium gathered 59 papers from 12 countries and was attended by approximately
400 engineers, scientists, and architects--f irmly justifying this type of conference. The papers pre-
sented Include those which are highly theoretical as well as those which describe popular programs.
Nine sessions were required during three days to present all of these papers. In addition, a technical
forum was held one evening to exchange Informal opinions on computerized controls. This was well at-
tended. It is hoped that this symposium made a major contribution to environmental engineering design
and these proceedings will be useful to all using computers in this field. The program committee will
welcome reactions and suggestions as an aid to planning future conferences of this kind.
T. KUSUDA, Chairman
Program Committee
IV
General Committee
P. R. Achenbach, Chairman
F. J. Powell, Vice-chairman
A. T. Boggs, Vice-Chairman
J. R. Ahart, APEC (U.S.A.)
J. M. Anders, ASHRAE (U.S.A.)
R. Cadiergues, (France)
W . Caemmerer , (Germany )
B. Givoni, (Israel)
J. L. Haecker, NBS (U.S.A.)'
I. Hoglund, (Sweden)
G. Wil,
K. Kimura, (Japan)
V, Korsgaard, (Denmark)
T. Kusuda, NBS (U.S.A.)
A. G. Loudon, (England)
H. F. T. Meffert, (Netherlands)
R. W. Muncey, (Australia)
C. W. Phillips, NBS (U.S.A.)
K. R. Rao, (India)
R. H. Tull, ASHRAE (U.S.A.)
J. F. Van Straaten, (South Africa)
, (Canada)
V
Program Committee
Dr . T . Kusuda , Chairman
Room A307, Building 226
National Bureau of Standards
Washington, D. C.
Professor Eugene Stamper, Vice Chairman
Department of Mechanical Engineering
Newark College of Engineering
Newark, New Jersey
Dr. D. G. Stephenson
National Research Council
Division of Building Research
Ottawa, Ontario, Canada
Mr. Metin Lokmanhekim
GARD/GATX
N. Natchez Avenue
Niles, Illinois
Mr. D. L. Richardson
Arthur D. Little, Inc.
Acorn Park
Cambridge, Massachusetts
Mr. H. C. S. Thorn
ESSA
Room 716, Gramax Building
13th Street
Silver Spring, Maryland
Mr. E. M. Barber
Room B309, Building 226
National Bureau of Standards
Washington, D. C. 2
Dr. F. G. Shuman
Director
National Meteorological Center
Room , FOB-4
Suit land, Maryland 2
Mr. Z. 0. Cumali
Consultants Computation Bureau
594 Howard Street
San Francisco, California
Professor J. B. Chaddock
Mechanical Engineering Department
Duke University
Durham, North Carolina
Professor L. 0. Degelman
The Pennsylvania State University
Department of Architectural Engineering
University Park, Pennsylvania
Mr. B. E. Birdsall
Ziel-Blossom and Associates, Inc.
700 Walnut
Cincinnati, Ohio 452 02
Mr. W. A. Schmidt
Office of Construction
(08H) Veterans Administration
Central Office
810 Vermont Avenue, N. W.
Washington, D. C. 2 042 0
Mr. J. Marx Ayres
Ayres, Cohen & Hayakawa
South Beverly Drive
Los Angeles, California
Arrangements Committee
C. W. Phillips, Chairman B. Steele
J. Szabo, Vice-Chairman S. Torrence
W. Carroll
VI
Contents
Abstract
Foreword
Preface
Members of General Conrmittee
Members of Program Committee
Members of Arrangements Committee
PLENARY SESSION
Chairman: P. R. Achenbach
National Bureau of Standards
1. Welcome Address
Dr. F. K. Willenbrock
Director, Institute for Applied Technology
National Bureau of Standards
2. Keynote Address: Some Objectives for the Technological Man
Bruce J. Graham
Skidmore, Owings and Merrill
COMPUTER GRAPHICS
Co-chairmen: J. B. Chaddock
E. M. Barber
3. An Insight Into Three Dimensional Graphics
A. R. Paradis
Dynamic Graphics, Inc.
San Francisco, California
4. The Use of Graphics in the Development of Computer-Aided
Environmental Design for Two-Storey Houses
A. Bijl, T. Renshaw and D. F. Barnard
University of Edinburgh
Edinburgh, Scotland
5. Anticipatory Techniques for Enhancing Remote Computer Graphic
T. N. Pyke
National Bureau of Standards
Washington, D. C.
6. Computer Graphic Data Structures for Building Design
M. Abrams
National Bureau of Standards
Washington, D. C. 2
VII
MODELING, DESIGN, SURVEY AND LINEAR PROGRAMMING
Co-chairmen: Z. 0. Cumali
J. Marx Ayres
« 7. A Systems Model for Environmental Design of Buildings 61
C. L. Gupta
CSIRO
Highett, Victoria, Australia
8. Design Considerations for a Practical Heat Gain Computer Code 71
S. F. Nermann and N. E. Mutka
DERAC Consultants, Inc.
Mercer Island, Washington 98OA-0
^ 9. Solving the Communication Problem in a Computer-Controlled 87
Environmental System
T. Prickett, J. L. Seymour, D. L. Willson and R. W. Haines
Collins Radio Company
Dallas, Texas 752 07
10. A Linear Programming Model for Analyzing Preliminary Design Criteria
for Multizone Air Distributions Systems 95
R. A. Gordon
Cornell, Howland, Hayes and Merryfield
Corvallis, Oregon
11. A Conceptual Survey of Computer-oriented Thermal Calculation Methods ^03
C. L, Gupta, J. Spencer and R. Muncey
CSIRO
Highett, Victoria, Australia
12. Method for Thermal Calculations Using Total Building Response Factors
R. Muncey, J. Spencer and C. Gupta
CSIRO
Highett, Victoria, Australia
13. Calculation of Building Thermal Response Factors (BTLRF)
as Wiener Filter Coefficients
T. Kusuda
National Bureau of Standards
Washington, D. C. 2
ANALOG COMPUTATION & TIME SHARING
Co-chairmen: L. 0. Degelman
E. M. Barber
14. Thermal Studies by Electrical Simulation. Application example to the
study of the heating equipment of an apartment building heated by
electricity 127
J. Anquez and L. Bertolo
CSTB
Champs-sur-Marne 77, France
VIII
15.
Analog Computer Simulation of an Air Conditioning System in a Com-
mercial Building Incorporating Yearly Weather Data
147
J. Magnus sen
Honeywell, Inc.
Minneapolis, Minnesota
16. Experience with a Thermal Network Analysis Programme Applied to Heat
Flow in Buildings 159
N. Sheridan
University of Queensland
Brisbane, Australia
17. A Method of Computer Simulation Through Modified Signal Flow Graphs
and Operator Concepts and Its Application to Syntheses of Heating
Equipment Capacities 171
S. Matsuura
Hokkaido University
Sapporo , Japan
18. Shared Time System Computer Programs for Heating and Cooling Energy
Analysis of Building Air Conditioning Systems 181
C. J. R. McClure and J. C. Vorbeck
Mechanical Engineering Data Services, Inc.
St. Louis, Missouri
ENERGY LOAD CALCULATIONS
Co-chairmen: E. Stamper
W. A. Schmidt
19. The Program of the ASHRAE Task Group on the Determination of
Energy Requirements for Heating and Cooling Buildings 199
R. H. Tull
ASHRAE Task Group on Energy Requirements
for Heating and Cooling Buildings
Lebanon, New Jersey
♦ 20. Successful Applications of Energy Analysis Programs 205
K. M. Graham
Southern Counties Gas Company
El Monte, California
21. Comparison of a Short Form Load and Energy Program with the
Detailed Westinghouse Load and Energy Programs 213
B. G. Liebtag and J. R. Sarver
Duquesne Light Company
Pittsburgh, Pennsylvania
22. Energy Estimating - How Accurate? 217
R. Romanchek
Pennsylvania Power and Light Company
Allentown, Pennsylvania
IX
23. Instantaneous Cooling Loads by Computer Based on ASHEAE's Time
Averaging Method 225
R. V. Thomas
Naval Facilities Engineering Command
Washington, D. C.
24. Computer Method for Estimating Net Energy Requirement for Heating
Buildings 229
N. E. Hager
Armstrong Cork Company
Lancaster, Pennsylvania
25. The Practical Application of Small Computers for Heating and Air
Conditioning Load Evaluation 241
T , Romine
Romine and Slaughter, Inc.
Fort Worth, Texas
26. Accuracy Requirements for Computer Analysis of Environmental
Systems 263
R. Cook and J. A. Serfass
Westinghouse Electric Corporation
East Pittsburgh, Pennsylvania
27. Calculation of Energy Requirements with the Proposed ASHRAE
Algorithms for U.S. Postal Buildings 279
M. Lokmanhekim
GARD/GATX
Niles, Illinois
289
28. An Accurate Computing Method for the Analysis of the Non-
Steady Thermal Behavior of Office Buildings
S. Oegema and P. Euser
Institute of Applied Physics, TNO-TN
Delft, Postbus, The Netherlands
29. A Successive Integration Method for the Analysis of the
Thermal Environment of Building
N, Aratani, N. Sasaki and M. Enai
Hokkaido University
Sapporo , Japan
30. Digital Simulation of Building Thermal Behavior ^■'•^
M. J. Wooldridge
CSIRO
Highett, Victoria, Australia
31. A Computer Programme for the Calculation of Individual Room
Air Temperature of Multi-Roomed Buildings ^27
K. Rao and P. Chandra
Central Building Research Institute
Roorkee, India
32. A Practical Method for Calculating Room Temperature Heating
Load and Cooling Load of a Multiroom
K. Ochifuji
Hokkaido University
Sapporo , Japan
X
33. Simulation by Digital Computer Program of the Temperature
Variation in a Room
G . Brown
The Royal Institute of Technology
Stockholm, Sweden
ENERGY CALCULATIONS, AIR DUCT SYSTEMS
Co-chairmen: D. L. Richardson
B. E. Birdsall
34. Optimization of an Air-Supply Duct System
W. F. Stoecker, R. C. Winn and C. 0. Pedersen
University of Illinois
Urbana, Illinois
35. Computerized Calculation of Duct Friction
H. F. Behls
Sargent and Lundy, Engineers
Chicago, Illinois
36. Pressure Loss Coefficients for the 45-Degree Return Air Tee
H. F. Behls and W. K. Brown
Sargent and Lundy, Engineers
Chicago, Illinois 606 03
37. Automatic Design of Optimal Duct Systems
M. Kovarik
CSIRO
Cheltenham, Australia
38. A System of Computer Programs Widely Used in Europe for De-
signing, Selecting and Analyzing Different Air Conditioning
Systems
A. Boeke and S. Larm
Technische Hogeschool, Leerstoel
Delft, Holland
39. Standardized Method for Optimizing Building Construction and
Heating and Ventilating Installations for Various Indoor
Climate Criteria
A. Boysen and S. Mandorff
National Swedish Institute for Building Research
Stockholm, Sweden
40. Designing Installations by Computer in Sweden
L, Sundberg
Wahling's Installation and Development Company
Danderyd , Sweden
41. A Cost Analysis Service Helps Optimize Building Costs and
Environmental Benefits
J. T. Malarky
PPG Industries
Pittsburgh, Pennsylvania
393
405
415
423
XI
42.
Comparative Computer Analysis of the Thermal Cost Performance
of Building Enclosures
437
W. A. Oberdick
University of Michigan
Ann Arbor, Michigan
SOLAR EFFECTS
Co-chairmen:
AND CONVECTION
F. G. Shuman
H. C. S. Thorn
43. A Numerical Method for Computing the Non-Linear, Time Dependent,
Buoyant Circulation of Air in Rooms 451
J. E. Fromm
IBM Corporation
San Jose, California
* 44. Fortran IV Program to Calculate Absorption and Transmission of
Thermal Radiation by Single and Double-glazed Windows 465
G. P. Mitalas and J. G. Arseneault
National Research Council
Ottawa, Canada
ts 45 . A Computer Analysis of Window Shading Coefficients by Calculating
Optical and Thermal Transmission 477
I. Isfalt
The Royal Institute of Technology
Stockholm, Sweden
46. Optimum Shape of External Shade for the Window to Minimize
Annual Solar Heat Gain and to Maximize View Factor 487
K. Kimura
Waseda University
Tokyo, Japan
47. Calculation of Smoke Movement in Buildings 501
T. Wakamatsu
Building Research Institute
Tokyo , Japan
*» 48. Use of Actual Observed Solar Radiation Values in the Determination
of Building Energy Requirements 519
J. Thies
Southern Services, Inc.
Birmingham, Alabama 352 02
XII
AIR CONDITIONING CALCULATIONS AND WEATHER DATA
Co-chairmen: M, Lokmanhekim
D. L. Richardson
49. Design of Direct -Expansion Evaporator Coils by Digital Computer 525
D. G. Rich J. B. Chaddock
Carrier Corporation Duke University
Syracuse, New York Durham, North Carolina
50. Simulation of a Multicylinder Reciprocating Refrigeration System
with Chilled Water Coil and Evaporative Condenser 545
E. Stamper and M. Greenberger
Newark College of Engineering
Newark, New Jersey
51. Use of Digital Computers for the Heat and Mass Transfer Analyses
of Controlled Environment Greenhouses 557
M. K. Selcuk
Orta Dogu Teknik Universitesi
Turkey
52. Automated Design Program for Air-Handling Apparatus 579
M. Nagatomo, S. Tanaka and N. Tohda
Kajima Institute of Construction Technology
Tokyo , Japan
53. Computer-aided System for Preliminary Air Conditioning Design 589
E. Maki and Y. Okuda
Nikken Sekkei Komu Company, Ltd.
Osaka , Japan
54. Computer Selection and Evaluation of Design Weather Data 603
E. N. Van Dev enter
National Building Research Institute, CSIR
Pretoria, South Africa
* 55. Quality Rules for Thermal Performance of Low Cost Dwellings
(Building Climatology for Argentine) 613
R. Alvarez Forn and I. Lotersztain
INTI
Buenos Aires, Argentina
WALL CONDUCTION AND THERMAL LOAD SIMULATION
Co-Chairmen: D. G. Stephenson
T. Kusuda
56. Fortran IV Program to Calculate z-Transfer Function for the
Calculation of Transient Heat Transfer Through Walls and Roofs 633
C. P. Mitalas and J. G. Arseneault
National Research Council of Canada
Ottawa, Canada
XIII
57. Application of Multilayer Periodic Heat Flow Theory to the Design
and Optimization of Roofing Systems 669
C, Smolensk!, E. Halteman and E. M. Krokosky
Pittsburgh Corning Corporation
Pittsburgh, Pennsylvania
58. Pulse Transfer Function and Its Application Related to Buildings 687
H, Yamazaki
Kyushu Institute of Design
Kyushu , Japan
59. A Calculating Method for Heating Loads of Buildings 693
Y. Nakazawa
Kyoto Technical University
Kyoto, Japan
60. An Example of Heating and Cooling Load Calculation Method for Air-
Conditioning of Building by Digital Computer 715
S. Kuramochi
Taisei Construction Company, Ltd.
Chou-ku, Tokyo, Japan
^ 61. Heating and Cooling Load Calculations by Means of Periodic Window
Function 745
K. Eguchi
Building Research Institute
Ministry of Construction
Tokyo , Japan
62. Banquet Address: Computers and the Building Industry 787
S . Daryanani
Syska and Hennessy, Inc.
New York, New York
XIV
Good morning.
Welcome to the National Bureau of Standards. I am substituting for the Director, Dr. Branscomb,
who unfortunately will be unable to greet you in person.
The Bureau has a deep interest in this First Sympositam on the Use of Computers for Environmental
Engineering Related to Buildings. We are pleased to be one of the three sponsors; we are happy to be
your host. While you are here we hope that you will find time to meet and talk with our staff, and
that you will take advantage of the tour of your facilities. I said your facilities to the American
taxpayers present because the Bureau is a tax-supported public institution with a goal to "strengthen
and advance the Nation's science and technology, and to facilitate their effective application for the
public benefit" .
The National Bureau of Standards from its inception in has been closely involved with build-
ing research and technology. In the early days buildings were not viewed from a systems standpoint
and the work was organized in response to specific, recognized needs for technical information on the
properties of building materials .
As early as , the Bureau had a 100-thousand pound testing machine which was used to measure
the strength of structural materials, such as steel and concrete. Later, the Bureau joined with the
National Fire Protection Association and the Underwriters' Laboratory in a program from which flowed a
large amount of data on the fire resistance of materials. These data were subsequently incorporated
in fire and electrical codes throughout the country.
1
In , these scattered activities were combined by the Secretary of Commerce, at that time
Herbert Hoover, into a Division of Building and Housing. The functions of the Division were to coordi-
nate scientific, technical, and economic research on building; to aid in the revision of state and mu-
nicipal codes, and to engage in the simplification and standardization of building materials. Despite
these broad goals, the primary effort remained in the materials evaluation area, and the application of
the findings to building codes and standards based on materials specifications. During this period,
however, there was a small but growing program concerned with the environmental conditions in housing.
The first attempts to study the habitability of housing could also be considered as the exploratory
examinations of buildings from a systems standpoint.
During the 's, the emphasis was on a "Better Homes Program". In the depression of the 's,
the Better Homes Program became low-cost housing; in World War II, the conservation of scarce building
materials was the major effort. After the war, for fifteen or so years, the building research programs
again stressed the properties of various kinds of building materials, with the exception of the environ-
mental work which continued in the direction of a systems approach to building problems.
But the winds of change have influenced even the Bureau, and today in our building research and
technology program we talk primarily about building systems; we are challenged by the problems of
evaluating the function and performance of buildings as they satisfy the user. We are still concerned
with materials, but view them as components which are part of a system. Our efforts are toward the
development of performance requirements and performance evaluation techniques for building components
and systems. Such efforts are compatible with the national trend toward industrialized building con-
struction.
The development of standards based on performance, and the consideration of buildings as systems
requires the evaluation of masses of data which are orders of magnitude larger than required for the
earlier materials evaluation or specifications studies. It is clear that the computer has influenced
our investigations in many fundamental ways and it is my prediction that it will have an increasing
impact on our thinking about building systems in the future.
A good Ph.D. subject for a student of the history of technology would be to determine how much
the change in our perceptions of buildings has been influenced by the availability of the computer as
a data and information-handling device.
Even today we are well past the relatively simple use of computers for the analysis of masses of
data. During this symposium we shall hear how computers are used in modeling or design studies related
to the environment of buildings; how they are used for evaluating the non-steady thermal behavior of
office buildings, how they are used for the design of heat /air-conditioning installations.
2
Our speakers in this symposium come from 11 foreign countries and from all across the United
States. They represent industry, the research community, the universities, and government. We shall
hear from architects, engineers, computer specialists, systems analysts, and from those in other disci-
plines. Indeed, this symposium program is Indicative of how computers are stimulating a "quiet revolu-
tion" in the building technology field. What is being done in this segment of the building process
points the way to what must inevitably be the norm for the entire building process.
So welcome once again to the Bureau, and to this First Symposium on the Use of Computers for En-
vironmental Engineering Related to Buildings. It Is our hope this symposium will provide an effective
forvun for the exchange of Ideas in the field. It is our hope that these sessions will stimulate others
to explore how computers may be used throughout all parts of the building process.
3
A recent article in Time MaRazine pointed out that the Unisex Society developing in the United
States is a s3miptoin of the decay of our civilization. As ultimate proof, it indicated that out of two
thousand previous civilizations - fifty five which suffered of this same symptom - such as the Greek
and the Roman eventually disappeared. I would propose that the other nineteen hundred and forty five
also disappeared or at least there is no evidence of their existence today.
The rise and fall of civilization has very little to do with the morality of those civilizations.
It becomes important to define what we mean by civilization. In Webster's dictionary definitions read:
"the condition of being civilized; social organization of a high order, marked by advances in the arts,
sciences, etc.; the total culture of a people, nation, period, etc: as, the civilization of the Occident
differs from that of the Orient". And finally, "the countries and peoples considered to have reached a
high stage of social and cultural development.". I contend that the American people do not fall under
any of those definitions. We certainly do not have order nor have we reached a high stage of social
and cultural development. In fact, there may never be an American civilization. I believe that we are
engaged in the process of developing a single civilization throughout the world - one in which America
will play a very important and, I hope, responsible role. Other nations have contributed in great
measure and will continue to do so. We are in fact children of past civilizations from Greco-Roman,
from African, Mayan and Chinese ancestries. It is, therefore, nonsense to talk gloom and doom when we
are barely participating in the dawn of this emerging culture.
The technological equipment today is breath-taking in scope. We have been able in the last thirty
years to break through barriers of exploration which did not exist one hundred years ago. Yet, we have
failed miserably on this earth in the efforts that deal with the problems of an ever-expanding popula-
tion. Recently man has created the first reproducing cell, but he has been unable to control the re-
production of man. We have created a completely antiseptic environment that can hurdle into space at
unbelievable speed - returning to earth with a relative safe and healthy human specimen, but we have
5
been unable to provide even the most basic of housing needs for the great majority of people of the
world.
It matters little what political system we support, what nations we swear allegiance to - singly
or jointly all nations have failed. The promise in America that capitalistic democracy would achieve
individual freedom is a myth. The much touted equality of communism is a fiasco and the self-serving
smugness of Scandinavian countries exists only at the expense of suffering millions around the world.
We are all aware of the usual capability of nations to wage war, regardless of financial stability.
Starving millions find no food, but plenty of guns with which to serve militarist demagogues.
Of paramount importance in our time is not the search for the secret new technology or the wonder-
ful do-all material, but the philosophical leadership which will redirect the great energy being expended
for the benefit - rather than the detriment - of people. There is hardly a technical problem existing
that cannot be solved, but equally there is hardly a solution in sight for the sufferings in the world.
No leaders plead the case for civilization.
The City today is hell bent on disaster. This phenomenon exists, by no means, only in America.
It matters very little whether we speak about a socialistic or capitalistic nation. Technocratic
achievement and production have become the paramount value. Other values are secondary. The cries
and, in fact, the screams of a few have had very little effect on the relentless progress of produc-
tion for the sake of production. It matters little what we produce, so long as we feed labor and raw
materials to the machine. As a result other values cannot be served. The typical urban center is
plagued with a series of fantastic problems - pollution, not only of the air and the water, but pol-
lution of sound - of vision - of taste - and of mind. Transportation is a story book of failures.
Tokyo, like New York City and London are reaching the point of standstill. The customary jokes about
traffic jams in Rome and Paris are no laughing matter to the Romans and Parisians. Tempers have risen
on this subject alone to a point of no return. Transportation has created and fostered economic
segregation; the poor in the cancerous center, the middle class in the greenbelt.
The university - once a sacred place - is in complete disarray everywhere. It matters little
whether we speak of disillusionment of the student at the Sorbonne, Kent University or the University
of San Marcos in Lima. The academy is no longer believable. Academic isolation has led to irrelevance.
Yet we know, or have faith that solutions could be found and that these solutions will depend heavily on
our technological baggage. This premise has been held for some time, but our credibility has lapsed.
The philosophical evaluation of priorities has eluded our grasp.
6
Much has been said about the expanding population of the world, and this is a problem. Much has
been said about the depleting resources of the world, and this is a problem; but little recognition
exists that it is not expansion in numbers alone, but rather the accelerated increase in ambitions
which cause the confrontations we now experience. The wandering Arab is no longer happy to wander.
The potato-growing Quechua Indian is no longer happy with a diet of potatoes. The millions of India
are no longer happy with an 18-year life span. In fact, not even the people of Wales are satisfied
with 2nd-class citizenship.
We do not need any more automobiles from General Motors or from Volkswagon or from Toyota. The
people need a healthy environment first, and it is not up to the leadership to deny it. The advertising
campaigns which are used to sell unnecessaries should now be used to sell the necessaries.
Poll-taking as an excuse for leadership is the instrument of the present political scientist.
This method will lead to continued mediocrity and worse. Ask a drug addict what he wants, he will
say drugs. Ask a hunter, he will say guns, but we need neither drugs nor guns. It seems inconceivable
that in this day we can produce models of the human body in a computer and measure the good and bad
effect of environmental inputs. Yet we cannot decide once and for all what is a good diet - what kind
of air we should breathe - what kind of noise we can bear or what kind of environment we can survive
in. The priorities of the modem economist do not recognize the primacy of human life.
It may become important at last that we begin to make value commitments, for the survival of
existing governments, universities and intellectual leadership will depend upon their ability to commit
the energies of human kind immediately towards the needs for survival. The pressure towards such
commitment will not come from the fickle and easily converted popular movements. Those are easily
swayed by Madison Avenue advertising or Latin American demagogues. Each and every educated man must
mold his well trained efforts towards the simple realities that face the world. This individual effort
can have tremendous influence since it is the technocrat who controls the valves of cornucopia. It
wasn't Hitler or Churchill or Roosevelt or Stalin who invented the atom bomb, but it is their out-
moded heritage that is rattling that frightening instrument.
Architects and planners of the last twenty years have been pre-occupied with their profession.
They are designers of objects. It appears today that they have proven without a doubt their own
irrelevancy. Walter Gropius many years ago decried the lack of involvement by architects epitomized
by the Ecole Beaux Arts in Paris - the Aesthetic of the Renaissance was but a symptom of the selfish
role the professional had carved unto himself. The Bauhaus movement of the 20 's in Germany was a
successful attempt to convert the industrial machinery into a viable architectonic language. Mies
van der Rohe epitomizes that success. In his hand the products of modem man became a poetry of space.
However, his lingo combined with the virile language of Corbusier - has been converted into a substi-
tute for the cliques of the renaissance. We are now extremely capable modern temple builders, except
that we care little what gods dwell in our temples. Our works are terribly important and, since they
7
serve the Images of false gods, they curse the life of the urban dweller around them.
Architects and planners have to turn about and realize that we are but transitory instruments in
the evolution of cities. Instant civilization is not about to happen - we are just barely defining the
kind of civilization we expect to create. We know that in such a civilization national boundaries do
not exist. Isolation from the dynamic world forces is impossible and existing political systems are
obsolete. All people of the world must participate, for in exclusion we seed discontent, and in segre-
gation moral decay.
The larger picture of the world affects the life of every individual and we must be prepared to
meet both ends of this candle. Some glimpses of such a society are possible. We know that the individual
citizen must participate in those decisions that affect his immediate life and that of his family. He
must, therefore, have something to say about where he lives - the school that his children attend - the
work he does, but on the other hand, he must enjoy the fruits of international medical research, the
writing of poets - the art of painters and scultors - the pleasures of travel - free air - all these
which cannot 'come about through micro systems, but that belong to larger structures.
Computer technology, if it has any promise, is this: it can make available to an individual the
knowledge of all; and the ability to make decisions at the most personal of levels under that larger
umbrella of knowledge. It is that promise which must direct the efforts of your conference.
I would propose to this conference that the papers presented here and at future conferences should
concentrate on the problems that face the urban centers of the world:
1. On Transportation - not how to move people, but how a city can exist, expand and grow
without the convulsion of movement we now enjoy. How can man live near his place of
work - near his children - breathe free air? Today that freedom of choice is denied.
2. What is a house - what kind of a house does a family need - what kind of environment
and air should children breathe - what kind of neighborhood does this house belong
to - how can a man move from one stage of life to a later one without the loss of
ties to his family and to his tribe?
3. What kind of diet does man need - how can this be distributed equitably from the
farmer to the dinner table?
4. Medicine - should not be the hunting ground for doctors. How do we provide medical
care for all, but more important, preventative medical care so that healthy lives
can be a backbone for fulfillment. As an example - humidified air is now the
privilege of machine environment, but shouldn't the delicate nasal passage of
children be protected?
5. In the integrated community how do we distribute the benefits of culture - music - dance -
theater - art - and all the other fulfilling human experiences, so that they become a
part of all peoples' lives - rather than the privilege of the few?
6. How do we maximize the fruits of this earth - preservation of forest - clean rivers
and lakes - in fact clean oceans? How should the resources be protected?
7. Education is an integral part of all the prior values, but how do we expand, elaborate
and create a meaningful civilization so that the recognized values of the intellectual
become the every day values of all citizens?
I propose that a conference such as yours should address itself to what end you work. It is not
important to develop a new program of heat transfer or of the design for sophisticated duct systems
unless that program is a meaningful part of the value set which makes up the fiber of our emerging
civilization.
The fracturized construction industry in America with its multiplicity of goals is only matched
in disarray by the even more fracturized Industry of construction in other parts of the world. Self
interest is the motivating force in construction. This force rules everyone connected with our labors
from bankers and land owners to government and labor unions. I was told five years ago by a high
government official that if architects do not respond to the crying needs of society, the government
would step in and solve it. At that time it seemed a ludicrous statement. Today, government's failure
to respond is even more obvious. The housing stock in America is depleting at a faster rate than anyone
will recognize. We have even gone so far as to substitute trailer and trailer parts for units of
housing. The trailer is not a viable housing - it Is sub-standard by anybody's definition.
For your work to become meaningful we must learn to make it part of a larger whole, we must
recognize that we are in the childhood of an emerging world civilization. For myself I find being
a part of this transition much more satisfying than believing we could be in the Golden Age.
9
An Insight into Three Dimensional Graphics
Arthur R. Paradis
Dynamic Graphics, Inc.
Computer graphics can be used to relieve much of the tedium
and time associated with the production of perspective drawings.
It frees the architects for more creative aspects of the design
process. It enables the architect to work closer with his client
through a constant flow of perspective drawings. There are prob-
lems associated with implementing such a graphics system. First,
the formatible image of the computer must be overcome. Then, a
simple project description process must be implemented. It must
be simple enough to use and flexible enough to make the system
worth using. Ideally, there would be a common data structure for
the graphics programs and the various engineering packages. Fin-
ally, there must be an efficient hidden line removal technique to
make the system feasible. Techniques are now developed which can
make such a system possible. Preliminary work done for Skidmore,
Owings & Merrill indicates that such a system can be an economical
and time saving tool. This paper will present the technical aspects
of three dimensional computer graphics: the basic tools; the struc-
ture necessary; and a comparison of hidden line removal techniques.
Key Words: Architectural Graphics, computer graphics, data
structure, hidden line removal, perspective drawings, pro-
jective geometry.
1. Introduction
Three dimensional computer graphics is becoming a cost-effective and time saving tool for archi-
tects and designers. Computer graphics allows architects and designers the freedom to study their lay-
outs with perspective drawings from more vantage points and to try more design variations than would be
otherwise possible with conventional means. This paper will introduce the basic tools of three dimen-
sional computer graphics, both software and hardware; discuss the various components of the structure
necessary for a three dimensional graphics system; and compare techniques for producing perspective
Figure la
Two views of San Francisco waterfront area
produced for Skidmore, Owings £■ Merrill
11
Figure lb
A computer generated perspective plot of the San
Francisco waterfront area showing a proposed
waterfront project
2. Basic Tools of Three Dimensional Computer Graphics
2.1 Software Tools
There are three basic software tools which are combined to provide a flexible system for producing
perspective drawings: the projection of lines in space, the representation of surfaces (topography), and
the portrayal of complex solid objects. Each area will be presented as current capabilities and as
advanced features which are being developed or are considered feasible.
a. Projection of Lines in Space
Lines in space may be represented by connecting a series of projected points with straight line seg-
ments. More advanced features allow the line to be represented by a smooth curve through the projected
points and permit the line to pierce surfaces or solid objects.
Figure 2
A projected line in space
12
b. Surfaces
Topography may be represented as a rectangular gridded mesh which may be displayed as a projected
mesh (fig. 3) or as a projected contour. It is not difficult to have either regular or irregularly
spaced grid lines. Thus, flat areas need not contain the same information density as rougher terrain.
It is more difficult to handle missing grid points. These may be computed by some interpolation process
or left as holes in the grid. Finally, there exists a whole series of functions which may operate on
either gridded data or randomly spaced data points.
Figure 3
A surface defined by a gridded mesh
c. Solids
Complex solid objects are generally represented by a series of bounded planar surfaces. The visible
portions of the planar boundaries are drawn with solid lines which the non-visible portions are generally
either blanked or drawn with dashed lines. For added flexibility, boundary lines can be specified as
non-visible and additional lines or patterns can be drawn on the face of any surface. Within the frame-
work of the basic system, curved surfaces must be approximated by a series of small planar surfaces.
More advanced features could include the ability to specify curved surfaces. Also, solid objects
could pierce each other. The amount of detail shown could be a function of the final viewing size such
that buildings or trees in the far distance would not be drawn to the same degree of detail as buildings
very close to the observation point.
Figure 4
Representations of solid objects defined by planar surfaces
2.2 Graphics Hardware
There is a wide range of graphical display equipment available which can be used at computer ser-
vice bureaus or purchased for in-house usage. The features, application areas, and price ranges for
various types of graphics equipment will be given below.
a. Pen Plotters
Pen plotters are computer driven pen and ink plotting devices. They are the most inexpensive and
most common graphics devices used. Pen plotters are available in a wide range of sizes from small drum
plotters to large flat bed plotters. Optional extra pens for different colors or line widths are also
available. Perspectives, plan views, PERT charts, etc. can be produced using pen plotters when used
with the appropriate software.
Price Range: $8,000 to $100,000 (including input device)
13
b. CRT Displays
CRT (Cathode Ray Tube) displays are becoming more popular. There are two basic types — the raster
scan CRT, which works much like a normal television set; and a vector CRT which draws lines in any
sequence. The vector CRT's are much easier to program for general graphics work as lines can be dis-
played as they are calculated. Some CRT's use a mini-computer for picture refreshing and local editing,
thus reducing the computer load and special software requirements of the main computer. Keyboards, light
pens, moveable cursors, and Rand Tablets are available as input devices for CRT displays. CRT displays
are valuable for providing quick results and effective data editing capabilities. They are capable of
providing general graphics output for applications which do not require high resolution, large display
area or hard copy (hard copy devices may be connected to a CRT).
Price Range: $10,000 to $250,000.
c. Microfilm Plotters
A microfilm plotter is basically a CRT display with a camera attached for producing hard copy.
They are ideal for creating computer generated movies. Hard copy can be directly produced or can be
made from the 16mm or 35mm film. The film is convenient for long term storage.
Price Range: $50,000 to $250,000.
d. Electrostatic Plotters
Electrostatic plotters produce a grid of dots. This type of plotter can produce either line plots
or render areas with a halftone effect. It has the potential for effectively displaying shadows.
Price Range: $12,000 to $50,000 (including input device)
e. Halftone Displays
The University of Utah has done a great deal of research into producing computer generated color
halftone pictures. These spectacular pictures are for the time being more of a laboratory tool and not
economical for most applications.
3. Structure of Three Dimensional Graphics
The structure of three dimensional graphics may be divided into four areas — Application Language,
Data Structure, Projective Geometry, and the Hidden Line Problem.
3.1 Application Language
The value of a graphics system, in this case an architectural system, lies with economic factors
and convenience. For an architectural graphics system to embody both flexibility and convenience, it
must be carefully interfaced with the architect in mind. Skidmore, Owings and Merrill are currently
working on this problem with encouraging results. The following shortcuts have proved very helpful
in simplifying the data description.
a. Implicit Relatsionships
The planes which define a rectangular block can be defined in more than one way. The easiest and
most cumbersome way is to define the coordinates (X,Y,Z) triplets for each of the six planes. This
would require the definition of twenty-four points (72 numbers) and would win few friends. By using
the implicit relationships of the orientation of the six planes of the rectangular box, it can be
defined by a height, width, length, location and orientation (the orientation can be implicitly defined
in many cases). This is defined by six numbers and is much more liveable.
b. Repetitive Definitions
A single window definition can be repeated to provide a whole face of windows or the windows for
the whole building. Similarly, the definition of a building can serve for similar buildings in the
site.
' , c. Predefined Objects
Trees, vehicles, people, surface textures, building complexes, and even areas of large cities may
exist as predefined objects in the architect's library.
14
mxziziiizzi
HJ II II -I
Figure 5
Windows are defined by patterns and the trees
are predefined objects
3.2 Data Structure
The resulting data structure should contain more information than just the definition of lines and
planes. Information about the logical groupings and any hierarchial structure will allow more powerful
editing and manipulation capabilities. The data structure should be flexible enough to interface with
engineering programs such as duct layout, space allocation programs, or heating and cooling load calcu-
lation programs with minimal additional information. Plan views and elevations can also use the same
data structure.
3.3 Projective Geometry
Both perspective projections and parallel projections are easily implemented. Perspective projec-
tions add realism to the drawings and the required mathematics is clearly presented by Kubert, Szabo and
Giulieri [1].^
3.4 Hidden Line Removal
Determining by computer which lines are "hidden" when viewing from a specific point is a very
challenging and frustrating problem. There exist various solutions, each tailored to a specific purpose,
such as surface algorithms, planar solid algorithms, etc., and these may be combined to efficiently
solve complex problems, but the resulting system is far from simple. Much work and possibly larger
computers are required before simple general algorithms can be developed which will process in a reason-
able time and at a reasonable cost.
4. Comparison of Surface Algorithms
Three different algorithms for solving the hidden line problem for surfaces will be compared. The
advantages and disadvantages of each will be explored and general statements describing the relative
efficiency of the algorithms will be presented.
Yd)
Y(2)
Y(3)
YCt)
zCi.i)
Z(2,l)
Z(3.1)
Z{4J)
Z(5J)
Zi\.l)
1(1.2)
Zf3.2)
7(U ?)
Z{5,2)
Z(l,3)
Z(2,3)
Z(3,3)
Z(it,3)
Z(5,3)
2(1.4)
Z(2,4)
Z(3,'*)
Z(4,4)
Z(5,4)
Example of structure of gridded mesh used in sur-
face definitions. In FORTRAN terms the structure
is comprised of an X array, a Y array and a doubly
dimensioned Z array; and the mathematical relation-
ship between the X, Y, and Z arrays is
Z(I,J) = f(X(I),Y(J))
where f is a single valued function.
X(l) X(2)
X(3)
X(4)
X(5)
Figure 5
Figures in brackets indicate the literature references at the end of this paper.
15
4.1 Aerospace Algorithm
TMs algorithm was developed by Ruber t, Szabo and Giulieri [1] at the Aerospace Corp.
a. Definitions
The point to be tested for visibility will be called the test point; the line between the observa-
tion point and the test point will be called the test line and the plane perpendicular to the X-Y plane
containing the test line will be called the test plane.
Figure 6
Test point, test line, and test plane
b. Basis of the Method
For a point to be non-visible, the test line has to pierce the surface. A brief step by step
method will be given below;
c. The Basic Algorithm
STEP 1: A series of test criteria points are calculated from the intersection of the test plane
and the gridded mesh. (Note: only the points between the test point and the observation
point are calculated.)
STEP 2; The test line divides the test plane into two sections. The test point is declared non-
visible if there is at least one test criteria point in each of the two sections of the
test plane; otherwise, the test point is visible.
STEP 3: When two adjacent grid mesh points are visible, the connecting line is drawn.
STEP 4: When a grid point is visible and the adjacent grid mesh point is non-visible, the
visibility, non-visibility transition point is calculated by using a binary search and
using the above steps to determine the visibility of the successive midpoints.
d. Advantages
This algorithm is easy to implement and requires a relatively small program.
e. Disadvantages
The execution time rises exponentially as the size of the defining grid mesh increases. There are
more test points and each test point requires the calculation of more test criteria points for the
visibility testing. (This exponential relationship became painfully clear when it was discovered that a
surface defined by 150 by 150 mesh points costs over $400.00 to compute.) This method also requires the
whole grid mesh to reside in memory at all times. Finally, the method does not always produce the exact
solution to the hidden line problem as steps 3 and 4 do not catch all changes of visibility.
4.2 Warnock Algorithm
This algorithm was developed by Dr. John Warnock [2] at the University of Utah. The following des-
cription does not do this algorithm justice as its real power lies in its ability to easily produce half-
tone pictures when coupled with the appropriate plotting equipment.
16
a. Definitions
Picture resolution will refer to the smallest distance between two adjacent points on the given
display device.
b. Basis of the Method
This algorithm uses an interesting method for solving the hidden line problem. An area of the pro-
jection plane is examined. If the method determines that the area is "simple" then it contains no visi-
ble line so processing is finished on that area; otherwise the problem is simplified by subdividing the
area into smaller sub-areas. The process is then applied to each of the sub-areas and reapplied until
the sub-area is either simple or the picture resolution is reached. If the picture resolution is
reached the square contains a visible line and the resolution sized area can be displayed as a dot.
Figure 7
Subdivision Process
c. The Basic Algorithm
STEP 1: For a given sub-area of the projection plane, determine the proper classification (out of
three) for each plane in the surface.
Case 1) The projected boundary of the plane surrounds the area of the projection plane
being considered.
Case 2) Part of the area of the projected surface overlaps with the area of the projection
plane being considered.
Case 3) The projected boundary of the plane lies totally outside of the area of the pro-
jection plane such that the two areas do not overlap.
Projected
Boundary
of
Pol ygo!
Pol ygon
Case 1
Case 2
Figure 8
Po ] ygon
Sub-area
Case 3
Three possible relationships betweeen sub-area
and projected boundary of a polygon
STEP 2: For each case 1 or case 2 plane, determine the distance from the observation point to the
plane at all four corners of the surface plane.
STEP 3: Determine whether the sub-area of the projection plane is simple. The sub-area is simple
if:
17
1)
The sub-area contains no planes of case 1 or case 2. It is blank.
2) There exists a case 1 plane which is clearly closer to the observation point than all other
case 1 or case 2 planes. A plane will be clearly the closest if the plane is closest to
the observation point at all four corners .
STEP 4: If the sub-area is not simple then subdivide it into four equal sub-areas and depending on
the size of the new sub-area either :
If the sub-area is larger than a the picture resolution, start with step 1 and process the
first new sub-area.
If the new sub-area is not larger than the picture resolution, then it contains a portion
of a visible line on the surface, so add the point to the display file.
If the sub-area is simple, it implies that no visible lines in the surface are contained
in that sub-area, so go on and process any of the other of the four sub-areas which remain
to be processed, or then process any of the sub-areas remaining in the next higher level
until the processing is finished.
d. Advantages
The algorithm works well with both surfaces and planar solids. Intersecting solids present no prob-
lem. Time for solving the hidden line problem is reasonable, although it could get excessive with a
large quantity of data. This is a good method for producing half tone pictures.
e. Disadvantages
This method works well only with CRT type displays as pen and ink devices use an extreme amount of
excess pen motion. Also, computer storage rises rapidly for large problems because each sub-area con-
tains two list of planes associated with it.
4.3 Horizon Method
This method was developed by the author at the University of California at Berkeley [3].
a. Definitions
Horizons — An upper and lower horizon delineate a closed opaque region.
Grid Line — The line connecting any two adjacent grid mesh points.
Mesh Element — Any four grid lines which form a closed rectangular box.
1)
2)
Visible Region
ypper
Hor i zon
Figure 9
Upper and lower horizons delineate
visible region from opaque region
Example of a grid line
and grid element
b. Basis of the Method
This algorithm uses the basic property that portions of a surface closer to the observation point
cannot be covered by portions of the surface more distant.
18
c. The Basic Algorithm
Figure 11
Sample grid to be processed
The surface is processed from near to far. The method presented is for viewing the surface from a
corner area. Other viewing areas require an additional step.
STEP 1: The edge row closest to the observation point will always be visible. It is plotted and
the projection of the edge row is used to define the opaque region.
Figure 12
Upper and lower horizons after first
row has been processed (identical)
STEP 2: The grid lines not already processed in the first mesh element (the bottom grid line would
have already been processed) of the next row are now processed. The lines are compared
with the opaque region defined by the horizons. The portions of the projected grid lines
visible are plotted, and the closed visible portions expand the definition of the horizons.
Figure 13
Upper and lower horizons after first grid
element of second row has been processed
STEP 3: The mesh element adjacent to the element just processed by step 2 is processed by comparing
plotting, and expanding the opaque region as in step 2. This process is continued until
each mesh element in the row has been processed. Steps 2 and 3 are continued for the
remaining rows .
Figure 14
Grid Lines compared with horizons and produced one
visible segment for this example
19
c . Advantages
Processing time is nearly a linear functions of the number of mesh points. The method also produces
the exact solution to the surface hidden line problem. Also, the whole surface need not reside in memory
at any one time.
d. Disadvantages
The algorithm is more difficult to implement and the actual program requires a larger computer.
4.4 General Observations for the Surface Algorithm Comparisons
a. To be economically feasible, solution times should not increase exponentially as the size of
the problem increases. This implies that the time required to test the visibility of a point
is independent of the size of the problem.
b. By using projected points for the hidden line removal, the last two methods were significantly
faster.
c. Using any pre-knowledge is also helpful for a faster solution, i.e., the inherent ordering of a
mesh surface can be used to advantage and further increase processing speeds.
5. Extensions into Solid Algorithms
Basically the same principles apply for the solid case that apply for the surface case. The three
surface algorithms each have their counterparts in a solid algorithm. The solid case is generally harder
since the implicit ordering of the gridded mesh is missing.
a. Extension of the Aerospace Algorithm
The basic test of visibility is modified to test whether a test line pierces any of the other planes
of the solid object. This can produce a tremendous number of tests and is definitely not feasible for
data representations produced from large quantities of data.
b. Extension of the Warnock Algorithm
The Harnock algorithm basically works equally well for both surfaces and solid representations. Any
solid program will process gridded surfaces with minor modifications as a surface can be represented by a
series of planes. However, since they do not take advantage of implicit ordering they are not as fast as
specialized surface programs.
c. Extension of the Horizon Algorithm
If the planes defining the solid object are ordered from near to far, then a series of small opaque
regions are defined as the planes are processed. Methods are being developed which minimize the effect
of having a large number of small opaque regions necessary for testing.
6. Conclusion
It is now possible to use computer graphics to produce perspective line drawings for a limited num-
ber of design applications which are cost competitive and produce drawings in a fraction of the time of
conventional methods. The sphere of feasible applications is growing rapidly and it will now be up to
the architects and designers to learn how to use this powerful new tool and to guide future developments.
7. References
II] B. Kubert, J. Seabo, S. Giulieri, The Perspec- [3] A. Paradis, An Algorithm for the Efficient
tive Representation of Functions of Two Var- Removal of Hidden Lines from Projected Sur-
Lables, JACM, Vol. 15, , pp. 193-204. faces. Tech. Report 34, University of Cali-
fornia, Berkeley, California, June .
[2] J. Warnock, A Hidden Line Algorithm for Half-
tone Picture Presentation, Tech. Report 4-5,
University of Utah, Salt Lake City, Utah,
May .
20
The Use of Graphics in the Development
of Computer Aided Environmental
Design for Two Storey Houses
Aart Bijl^ ^
Tony Renshaw and David F. Barnard
Architecture Research Unit
University of Edinburgh, Scotland
The Architecture Research Unit (ARU) is working on a two year research
project to develop the use of computers in the field of housing design and pro-
duction. This research is sponsored jointly by the Scottish Special Housing
Association and the Ministry of Public Building and Works. The ARU's task is
to develop a convenient technique for generating a description of the fabric of a
building, within a computer. This must convey the geometric information which
is traditionally contained in architects' drawings, in such a way that it remains
intelligible to the user and is also suited to the further attachments of topological
relationships associated with a variety of design considerations. Current use of
graphics by designers is being studied, to prepare for new and acceptable con-
ventions which are suitable for computer graphics input and output. It is now
possible to use the computer to design a house plan on a cathode ray tube display,
and introduce modifications to shape, size and building elements. This informa-
tion can be fed into a program to check for consequences on construction, thermal
environment, daylighting and other design properties which may be stored in the
computer's data structure. This paper considers the relevance of graphics in
an existing context of house design and production, and shows how this rele-
vance is maintained through the application of a computer aided design system.
Computer equipment currently being used on this project include a DEC PDP7
and 340 display with light pen, linked to an Elliott with disc backing. Hard
copy output is obtained from a Calcomp 563 incremental plotter. Application
of this research will be directed at two storey house production by the Scottish
Special Housing Association; and benefits may be expected in subsequent
improved ability to meet evolving environmental design requirements, to make
greater use of scarce professional services, and to facilitate costing and con-
struction of houses.
Key Words: Computer graphics, design practice, design process,
geometry, graphic conventions, housing, information structures, man
machine interaction, problem description, production information,
topology.
1. Introduction
Any benefit from the use of computers in assisting the solution of a problem is dependent on an
appropriate and clear description of that problem. The problem description needs to be un-
ambiguous and intelligible to the machine, whilst also remaining recognisable to the person who is
using the machine. In problems concerning environmental design relating to buildings, satisfactory
solutions are dependent on suitable means for describing buildings.
2 Research Architect
Architect/programmer and mathematician/programmer, respectively.
21
Prior to the availability of interactive computer graphics, building description for input to
computers required a lengthy process of identifying co-ordinate reference points relating to a
building's geometry. This information had to be compiled into long lists of numbers, unfamiliar to
the designer. The task of translating the building description into a form suited to computer
input (1) ^ required the skills and dedication of a specialised designer /programmer . This difficulty
is a principal cause of the slow and reluctant acceptance of computers by designers, in the building
industry.
The present object is to discover v/hether the opportunities provided by computer graphics
facilities are suited to closing the comprehension gap between designers and the machine; to see
whether designers may benefit from using computers as a general design aid, and so be encouraged to
accept its use in practice.
2. Design Functions
The process of designing buildings is sometimes described as a linear sequence of activities,
from inception of a new design through to completion of building (table 1) (2) and could continue
throughout the useful life of a building to the time of its demolition.
Stage
Table 1. Stages in Design Process (based on the RIBA Outline Plan of Work)
Usual Terminology
A. Inception
B. Feasibility
\
Briefing
/
1
C. Outline Proposals i
1
D. Scheme Design i
Sketch
Plans
/
Detail Design
F. Production Information
G. Bills of Quantities
H. Tender Action
1
Working
Drawings
I
I
J. Project Planning
K. Operations on Site
L. Completion
M. Feed-Back
Site
Operations
\
The linear sequence of these activities is readily questioned when considering the evidence of
practice, and observing the return loops and the lateral deviations which actually occur. But the
linear description is useful as a scale by which to refer to the particular levels of operation in any
system, to produce relevant indications of the kind of information which will need to be processed,
and the appropriate manner of presenting and conveying this information.
Using the scale A to M of table 1, and by reference to the work of others in the field of com-
puter aided design, it becomes possible to define the scope of the ARU's work. Some of the work
undertaken in Britain can be regarded as dealing primarily with production information after design
decisions have been taken (3), producing bills of quantities, ordering schedules and references to
standard construction details; operating from E to H. The other end of the scale is represented
by work on analytical processes which lead to early design decisions, relating the results of computer
1
Figures in brackets refer to the bibliography at the end of this paper.
22
analysis to single line design representations on a c. r. t. (4); and operating from A to C.
The field of application offered by the Scottish Special Housing Association, with its commitment
to build, places a bias on the ARU's work towards achievement of benefit at the production informa-
tion end of the design process. However, having the precedent of work produced by others in this
field and seeing difficulties in bridging the gap in operation between the design and production ends of
the scale, the ARU decided that it should attempt to operate within this gap and work outwards towards
both ends. Thus the ARU is currently operating from C to F, with the intention of allowing a
designer to build up a problem description in various ways, to respond to property analysis by the
computer relating to design decisions, and leading gradually towards specific and detailed production
information.
2. 1. Graphics related to Design Functions
Existing precedent in design practice indicates a relationship between the levels of specificacy
relating to stages in the design process and the form of graphics used to convey information (table 2).
The relationship of graphics to stages in the design process will vary, in response to varying fields
of application. Where the building type leads to repetition of relatively stable information, as in
housing, the link between a and c will occur early in the design process. Where complex and non-
repetitive building forms are involved, as in schools or hospitals, the progression from a to c is
likely to be more gradual. This is illustrated in table 3, which relates the use of different forms of
graphics to the applications fields of new housing, modification to standard housing and more complex
buildings .
Table 2. Association of Graphics with stages in the Design Process
Form of Graphics RIBA Stages
A to B
Diagramatic
single line
B to C
c. General Arrangement
double line
(locational reference
for detail information)
d. Detail Representation
complex graphics
(assembly information)
e. Component Information
C to H
E to H
E to H
Table 3.
Relationship of Graphics to stages in the Design Process effective in
different Design Fields
Stage
Design Fields :
New House
Design
Std. House
Modification
Schools
etc.
Inception
Feasibility-
Outline Proposals
Scheme Design
Working Drawings
Details
a
b c
c
c
c d
d e
c
c
c
c
c d
d e
a
a b
b c
c
c d
d e
The alpha characters refer to the forms
of graphics given in table 2.
The use of graphics represented by c under new and standard housing closely resembles
practice at the SSHA and is used to refer to the more variable information being accessed and
generated during design.
2.2. Communication of Information
In building design practice a number of particular circumstances exist which influence the
way in which information can be conveniently handled. The functions of storage and recall of
information are affected by the large variety of people with diverse motives and ability, who are
involved in building. The interdependence and interaction of a great variety of interests present
during design requires that any system cannot depend on a linear sequence of functions and must be
capable of entry at various points.
A designer's presentation of information normally consists of an assembly of previously
known bits of information, which make up a proposal, or instructions, for a new building. The
newness and relevance of a particular presentation exists in the relationship of one bit of informa-
tion to another; its presence, location and physical fit (5). In detail considerations this may
include shape; a new relationship of one surface to another which encloses a specified material.
This amounts to the geometric or topological information of or between objects or activities.
The different bits of known information contained in the assemblage are identified by the use
of conventions which are familiar to all the people involved. The convention enables each person
to recall the particular information which is being referred to.
The general predominance of geometric or topological information, as the meaningful content
in a designer's presentation of information, has formed the basis for extensive use of graphics.
This is true of the past, and if people are to continue being involved in building design and be in
control of their environment, then this dependence on graphics is likely to continue into the future.
2. 3. Computer Graphics
In order to devise new and acceptable conventions which are suitable as computer input and
output, it is necessary to consider first the current use of graphics by designers and relate this to
alternative vehicles for conveying information i.e. niimeric or verbal descriptions.
Verbal or numeric representations are built up by stringing together many characters or
numerals, either singly or in groups; and the association between characters or numerals is
governed by the operation of laws i. e. grammar or mathematics discipline. Each character alone
is meaningless, the combination of characters is made to be meaningful. This structure is absent
24
from most conventional graphic modes of presenting information; and it is this difference which has
led to the discrepancy between* the use of machine aids for alphanumeric information and the lack of
use of machine aids for graphic information.
SYMBOL
NOTATION
MECHANICAL
ELECTRONIC
"WORDS
NUMBERS
fingers
GRAPmCS
ABC
alphabet
2 3 4
numerals
^ ■
typewriter print
tables sliderule calculator
J
K I electronic _ computing
' memory system
hand
figure 1. The use of symbols or characters in combination to represent information, affecting
development of appropriate machine aids.
Computers must receive information in bits, each with prespecified relevance, which can be
compiled within a system to represent a whole assembly of meaningful data. In current design
practice information is presented by drawing lines by hand; each bit of line on its own conveying
little information to anybody other than the person doing the drawing. It is only as the drawing
develops that its information content becomes more meaningful. The hand drawn information does
not have to make sense until the drawing is complete. New graphic conventions need to be
developed which consist of separate elements, or bits, of prespecified significance, which can be
assembled to convey new and complex data. In this way a useful "grammar" for graphics should
begin to grow.
3. Field of Application
A two year research project has been undertaken by the Architecture Research Unit (ARU) of
the University of Edinburgh, which is being sponsored jointly by the Ministry of Public Building and
Works and the Scottish Special Housing Association (SSHA). The initial two years of research is
aimed at establishing the feasibility of applying computer graphics within an existing building design
organisation, to serve as a useful aid to the production of new buildings.
A narrow field of application has deliberately been chosen, to maximise the opportunity for
establishing principles of computer operation. If a satisfactory form of problem description can be
achieved, which is applicable to a narrowly defined design environment, then the principles of
operation which will have been developed should be capable of subsequent expansion to suit a wider
range of more complex applications.
The field of application is provided by the SSHA. This is an organisation which builds
approximately 5, 000 houses per year and is one of the largest house producers in Scotland. Most
of this housing consists of two- storey terraces, bviilt of "No-fines" concrete, though the total output
includes single and multi-storey houses and flats and includes brick construction.
The SSHA designs, manages and maintains the houses which it builds, usually on behalf of
local borough or city authorities. It provides all the professional, constructional and managerial
services associated with the entire life of its houses, within the one organisation. As such it
already has an exceptionally large store of information which should become readily available to
designers through the application of computers, to lead to informed decisions relating to new designs.
25
The great majority of house forms consist of simple rectangles with rectilinear internal sub-
division, on two floors of equal and constant storey height. The roofs are usually pitched, with tile
cladding. The range of materials and details used for construction are limited and there is little
variation in the required environment within houses. These small and simple building forms appear
to be ideally suited to standardization, both of design requirement and building product; but the
amount of variation which actually occurs at a detail level of specificacy, relating to construction
information, is extensive. The permutation of these detail variations within a whole house or
between one house and another gives rise to lengthy manual search procedures to check that all con-
sequences are accommodated in new construction information
3. 1. Graphic Requirements
The function of graphics is to convey geometric or topological descriptions; to provide
locations for bits of information; to identify the spaces which may contain material specifications.
Where the function of graphics is to describe a building to a computer, such problem
description should not anticipate or predetermine a solution. The graphics alone should not auto-
matically indicate a particular form of construction, but should allow free and gradual opportunity
for subsequent decisions leading to a specific design solution.
In providing geometric information graphics will tend to indicate relative size. This has to be
accommodated and controlled by the graphic conventions which are developed for the applications
context; the implied size accuracy should not be finer than person's ability to read off the viewed
image.
Given the context of SSHA houses, together with current national moves to co-ordinate all
height dimensions occurring within housing, it is possible to interpolate much of the three-dimensional
information required for building design and production from plans. In this context the need for
three-dimensional or animated computer graphic projections receives a low priority and it is possible
to concentrate effort on purely orthogonal projections.
A convenient form of building description input to computers could provide quick access to
computer analysis routines, which check the design for compliance with design standards or
regulations. Design alterations could be fed into a program to check for consequences on con-
struction, thermal standards, daylighting and other environmental properties.
Suitable computer input should enable cost information to be accessible at all stages during
design and this information could be continually updated by new information received from building
operations. Such use of computers should further provide output in the form of printed bills of
quantities, ordering schedules and intelligible working drawings.
3. 2. Equipment
The project team at the ARU has access to computing facilities in other University departments.
This consists of a DEC PDP7 and 340 interactive graphics display terminal with light pen, and a
Calcomp 563 incremental plotter.
The graphics terminal is connected by high speed link to an Elliott central processor,
with 64K word core and magnetic disc backing store.
In a design environment such as that of the SSHA, which does not yet practice the general
application of computers, fully interactive graphics may initially prove too expensive. The ARU is
therefore considering alternative cheaper and less sophisticated graphics facilities; and a parallel
research programme has been started which aims to develop the application of an ARDS direct view
storage tube, linked by delay line to an ICL System 4/75. The possibility of using a d. v. s. t. has
been taken into account in writing the program for the fully interactive graphics facilities.
The ARU has its own on-line Teletype terminal linked by voice grade line to a remote time
sharing bureau service, which is being used as a convenient form of computer access for interactive
program development.
26
4. Development of a Computer Graphics Application
Research work by the ARU on the application of computer graphics techniques to the work of the
SSHA is described in the following paragraphs and illustrations.
4. 2. Information Structures
The general data handling capability of computers is usually dependent on a precise and pre-
determined logic structure, so that it will make sense of any data it receives. In design practice a
similar methodical approach to handling information is sometimes attempted; but rules are often
broken. Where information passes between understanding people the method may appear to survive,
but where information passes to a computer any violated rules will cause a failure of the system. In
applying computers to the work of the SSHA, it is necessary to reassess the use of familiar informa-
tion structures, so that these may be modified to fit a computer's data structure; specifying those
areas of design activity which can best be handled by user interaction with a computing system.
In order to prepare for the need to process SSHA information through a computing system, the
ARU's approach to data structures has been to distinguish between different principal computer
functions. These differences are used to distinguish between the requirements of different data
structures. Each separate structure is developed to interrelate with the others but each is suited to
its own particular function. So far work has been based on distinctions between a graphics data
structure (GDS), an applications data structure (ADS), and a file handling system (LIBRARY).
The GDS notes the way in which points and lines come together on the screen, to represent
meaningful information to the user. It stores the relationships between the points and lines, and the
walls, windows, doors, rooms and surfaces which these represent; to which the user may want to
attach other non- graphic information.
■4-
COMPONENT
/K7^
ext
jnc
ext
jnc
^ROOM
surface
COMPONENT
/K/N
U
ti
u
1
J I L
surface
COMP.
ext
jnc
surfac e
figure 2. Example of an Applications Data Structure referring to a Room
27
The ADS holds the computer's pool of information which is received from the user and is
interpreted by reference to a permanent file of information stored on magnetic tape or disc. This
pool of information, which grows as the user builds up a design, is structured in terms of accom-
modation zones (floors), spaces (rooms), components (walls, windows, doors), surfaces and
junctions (fig. 2). The ADS has to note the relationships which exist between these items and has to
relate incoming information from the user to a corresponding stored item or group of items.
The computer has constantly to compare information received from the user with that already
stored in its LIBRARY, e. g. comparing component junctions with known working detail specifications.
It also sends information taken from the LIBRARY and qualified by the ADS to the user, e. g. ranges
of options for material specification displayed on the c. r. t. screen.
A request by the user to give or receive information is usually initiated by the user indicating a
point on the display. The computer uses the GDS to identify which item, or group of items, in the
ADS is being referred to. The computer then uses its immediate experience (the ADS) and its
LIBRARY to interpret the request, and supply or store the information relevant to the request.
4. 3. The Application
The representation of house plans on the c. r.t. is achieved by selecting graphic symbols which
can be used to build up graphic elements depicting walls, doors or windows. These elements then
serve as locating devices within the computer, for insertion of components of information.
The symbols are the basic graphic bits, rather like individual characters in an alphanumeric
presentation, which are used to assemble the graphics. Individually each symbol carries very
little information, other than an approximate indication of relative size and direction. A limited
range of five symbols is found to be s\afficient for representing the building fabric of houses (fig. 3).
A simple square is used to represent external or party walls and main internal loadbearing walls.
The same square bisected represents windows through such walls. The single bisecting line without
the square represents doors in the same walls. A smaller square is used to represent partition
walls, and a short straight line represents partition doors.
The first three symbols are used to fill 300 mm. square zones on a house plan and the last two
symbols fill 100 mm. zones. This corresponds to the nationally adopted incremental system of
300 mm. and 100 mm. for house building, accompanying the change to metric measures and the
introduction of dimensional co-ordination. These two dimensions are used in the computer appli-
cation to provide the basic order by which more complex graphics may be assembled.
Graphic elements are built up from symbols on the c. r. t. Each element (fig. 5) carries
information on the location, form, length and approximate width of a building element, e. g. wall.
The design environment may further allow interpolation of overall height, and the subdivision into
parts, e. g. window cill and head height. A number of elements can be assembled, changing the
symbol for windows, doors and partitions, until a complete house plan is produced.
A component of information refers to the data which the user wishes to associate with the
graphic element, which the computer receives into its ADS, and which may be filed in the LIBRARY.
Such a component may refer to conceptual properties or performance characteristics of the design,
e. g. the intended heat transference through a wall, or the required structural stability to withstand
given loading. A component may refer directly to a material specification, or partial specification,
for an element which constitutes a part of the building fabric. A graphic element does not necessarily
have to carry a component of information, it can be empty.
The figures 3 to 9 generally illustrate the procedure for assembling the graphic representation
of house plans on to the c. r. t. Plans may be modified, by deleting and rebxiilding one or more
elements (figs. 10 to 12); and plans can be stored by the computer on disc or paper tape for sub-
sequent retrieval and further modification. Hard copy output is provided by the digital plotter.
The facility for materials specification is considered to be a necessary part of the procedures
available to the user for describing a problem to a computer. Materials specification, as with
graphics representation, is optional to the user, depending on the particular computer analysis which
is to be performed on the problem description (fig. 17).
28
The user can build up a materials specification for a symbol or an element by selecting options
which appear as computer controlled menus on the c. r.t. He is guided through the process of
selection by messages which appear over the menus, which inform him of the stage of specification
which has been reached. In the case of walls the specification is made in three stages i. e. primary
material, external cladding and internal cladding (figs. 14 to 16). As each selection is made the com-
puter ADS references the LIBRARY in order to generate an appropriate subsequent menu, for display
and further selection.
If a symbol is selected for materials specification, the computer will generate an appropriate
menu of general primary options, followed by appropriate general internal and external claddings.
These tend to be short menus including only those materials which can be used whenever the symbol
is used to build up elements throughout a plan. When the user indicates a particular element for
materials specification the computer will generate appropriate menus containing specific options; and
these menus tend to be longer, containing the wider range of materials suited to specific locations in a
plan.
The specification for any symbol or element does not need to be complete; the user may select
the SKIP option in any menu to call the next menur, or select EXIT if he wishes to terminate the
specification (fig. 15). At any stage-of the development of the problem description the user may sub-
sequently return materials specification to modify or add to previous information.
The materials specification built up through user selection from menus displayed on the c. r. t.
assigns materials to a graphic representation of a house plan which is viewed at a scale of 1 : 50. As
soon as the specification refers to a number of adjacent elements the computer can assemble associated
data leading to' information on jimctions between components. The computer can then identify con-
struction details and recognise fit or misfit conditions. In the ARU application this information is
cross-referenced with manually prepared standard construction details which back up the computer's
store of information to allow the output of practical production information.
Operation of the system which allows the user to prepare and interact with the problem
description is illustrated in figure 17 and the various stages, or modes of operation, are explained
in the accompanying table 4. Lines linking the stages indicate a sample of possible routes through
the system; the continuous line showing an entry through the general specification of materials to
symbols, leading on to graphics; the dotted line showing an entry through graphics, leading directly
on to some analytical function or passing through specific materials specification; and the dashed
line showing an entry through modification of an existing problem description.
Figure 18 and the accompanying table 5 illustrate an example of one analysis function which can
be performed. This example is concerned with heating, and the analysis is structured to allow the
user to select alternative start points, and by varying the input data, to arrive at computed informa-
tion on either the temperature levels which will be maintained or the heat input which is required.
Where the desired result cannot be obtained by manipulating the variables ( D E G or J) in this
function, the user can return to modify the main problem description.
The major part of the ARU's research effort has concentrated on the development of an
operating system (fig. 17) which allows the designer to describe a building to a computer, introduce
modifications and build up information at various levels of specificacy; to prepare for the operation
of a wide range of computer analysis functions. This technique for problem description needs to be
tested for a wider range of applications, involving different and more complex building forms and
including the arrangement of grouped buildings.
29
CMtM UimM WIMT
O ■ — • mm mmt mat □ B - • ■ **■ tm mm
Mit ;RETllRM» mif 4NK «» mi RETURHv' ' ; kit RETURMr
figures 3 4 5, 6
Initially the display shows a planning grid representing 300 mm. squares, with five graphic symbols
and a number of light buttons displayed along the bottom. The user selects a symbol with a light pen
and tracking cross, and this is used to locate the extremities and corner positions of a graphic
element. If a graphic element representing a window is built up on the display, the user is given an
opportunity to specify particular height information.
figures 7 8 9
The user proceeds to construct elements to represent a house plan, completing the perimeter
boundary walls and proceeding with the internal subdivision. When the graphics is complete the
user can call up the space function which causes a display of room labels and he can proceed to
identify the spaces bounded by elements as rooms.
30
figures 10 11 12
The user can modify completed house plans, by deleting elements and selecting new symbols in
order to build up new and different graphic elements.
tnmex muum immtt Mun ■■■■•I tumm ■ tuiKt onniM.' eutom
iigures 1-1 ID 10
Material specification is carried out by selecting MATERIAL from a list of functions displayed on
the screen. The user identifies a symbol, or an element, with the light pen, and a range of
appropriate primary material options appear in the menu area, together with a message calling on
the user to make a selection. The menus are paged under computer control, for internal and external
claddings, until the specification is complete.
31
32
Table 4. MAN MACHINE INTERACTION - CAAD OPERATING SYSTEM
USER PARTICIPATION
STAGE LABEL
COMPUTER FUNCTION
User enters job reference
code
User indicates new pro-
blem
User indicates old
problem
User selects problem
description for display
User defines geometry and
topology of components of
the problem description, by
assembling graphic elements
on the c . r . t.
User modifies existing
graphics on the c. r. t. by
deleting and adding new
graphic elements
User labels spaces which
are described by graphic
elements
User can assign material
specifications to each or any
of the symbols before ele-
ments are assembled on the
c. r. t. ; the specification is
made by user selection from
menus, which appear on the
screen
A.
Enter
B.
New
C.
Old
D.
Display
E.
Draw
F.
Modify
G.
Space
H.,
Material
general
Computer uses user identity as control on
further information which will become available,
identifies existing project files and is ready to
create new ones, calls for description of pro-
blem: new or old?
Computer is ready to create new information
file; to receive new problem description for
translation into computer model.
Computer retrieves existing model from store,
deposits this in core; ready for display, modi-
fication or analysis.
Problem description is displayed on c. r. t.
Computer begins to assemble associative
model by restructuring elements into com-
ponents, surfaces and junctions .
Computer modifies existing model and checks
consequences on affected data already contained
in the ADS.
Computer defines the space by forming a ring
of surfaces to the components which form the
boundaries of the space.
As each symbol is indicated, the computer
searches the library file in order to build up
appropriate menus and store the selected
specification for subsequent entry into com-
ponents as graphic elements are input on the
c. r. t. ; this information can serve as a control
on later decisions by the user as the graphic
description proceeds.
User can assign material
specifications to displayed
graphic elements on the c. r. t.
User can indicate particular
analytical function which is
to be performed by the com-
puter on the problem
description
J.
Material
specific
K.
Functions
Computer enters data into the ADS and will over-
write data which may previously have been used
to describe the affected components; this infor-
mation can be made subject to controls, i. e.
recognition of fit between components.
Computer calls the appropriate analytical
routines into core, to operate on the model con-
tained in the ADS, and the first function is to
check whether the model is complete for pur-
poses of executing the required analysis; at
this point, or at any stage of analysis, the com-
puter can indicate the need or opportvinity to
return to any of the stages D to J.
33
figure 18
Function : HEATING
The arrows indicate a few of nnany possible routes through
the system.
Table 5. MAN MACfflNE INTERACTION - FUNCTION : HEATING
USER PARTICIPATION
User selects HEATING from
list of functions displayed on
the c. r . t.
A. function:
HEATING
Computer checks request against appropriate
completion of building model (problem des-
cription) already in the ADS, informs user if
not complete and awaits input of required
further data.
User indicates heating
evaluation relating to all the
space within external wall
boundary.
User indicates heating
evaluation relating to a
specific space
User specifies amount of
heat to be supplied to the
space
B.
Whole
Building
C.
Part
building
D.
Heat
input
Computer extracts information from ADS on
state of external walls.
Computer extracts information from ADS on
the state of the boundaries to the specific
space.
34
User specifies temperaiture
range to be maintained in
the space (against a given
external environment)
User calls for information
on previous decisions re-
lating to the problem
User can assign U values
to each or any of the symbols
User can assign material
specifications to each or any
of the symbols
User can assign U values to
each or any of the elements
User can assign material
specifications to each or any
of the elements
User calls for information
on the heating levels which
will be maintained, in
response to previously
entered data; the user may
return to modify data until
satisfactory heating levels
are achieved.
User calls for information
on the amount of heat input
which is required, in
response to previously
entered data; the user may
return to modify data until
a satisfactory figure for
the amount of heat input is
obtained.
E. Temperature
required
F.
State of
model
G.
U value
general
H.
Material
general
J.
U value
specific
K.
Material
specific
L.
Temperature
maintained
Computer tells user whether materials have
been specified for the boundary elements and
whether there are restraints on exercising
further options.
Computer enters data into the ADS at the
appropriate locations indicated by the graphic
elements on the c. r. t.
Computer searches the library file for speci-
fications which provide the required U value
appropriate to each symbol indicated by the
user; in order to build up appropriate menus,
and relate the selected specification to the
corresponding elements already existing in the
problem description; newly selected material
specifications will replace previous speci-
fications.
Computer enters data into the ADS; and over-
writes previously specified corresponding
data for the same locations with this new data.
Computer searches the library file in order to
btdld up menus which provide the required
U value (as for H above).
Computer checks whether input data is complete
and then proceeds to perform heating analysis
taking account of:
a) exterior temperatures
b) surface area of space
c) U values of boundaries
d) amotint of heat input
to arrive at figures which describe the heating
levels which will be maintained.
M. Heat
required
Computer checks whether input data is com-
plete and then proceeds to perform heating
analysis taking account of:
a) exterior temperatures
b) surface area of space
c) U values of boundaries
d) range of temperature to be maintained
to arrive at figures which describe the
amount of heat input which is required.
35
5.
References
D.J.O. Ferry; Measurement of Structural
Concrete Work by Co-ordinate Reference,
University of Southampton U. K. , CE/ 2/68.
Computer Development in West Sussex 1 and
2, Architects' Journal 21 and 28 February
, pages 421 to 426 and 489 to 493
respectively.
R. J. Stibbs and J. P. Steadman; A Computer
Aided System for Architectural Design
Analysis, reprint from Cambridge Research
U.K., Michaelmas .
(4) Handbook of Architectural Practice and
Management, Part 3. 220 Plan of Work,
Royal Institute of British Architects,
revised .
(5) Aart Bijl; Computer Aided Architectural
Design, paper to Computer Graphics 70 at
Brunei University U.K. , April .
36
Anticipatory Techniques for Enhancing Remote Computer Graphics
Thomas N. Pyke, Jr. ^
Center for Computer Sciences and Technology
National Bureau of Standards
Washington, D. C.
Techniques for enhancing the performance of graphical display
terminals located remotely from a central computer system and
connected by limited communication lines are discussed, with
emphasis on the system requirements of environmental engineering
applications. A set of mechanisms that anticipate a user's needs is
presented, including related techniques that have been used to support
computer graphics terminals and new ideas for optimizing display
operation.
Factors considered in this study of anticipatory techniques
include the effect of communication line loading and central system
response to requests from a local display- driving computer. Also
of interest are various ways for deciding what to anticipate and for
considering multiplexed communication lines. Extension into a com-
puter networking environment is also discussed. A few potential
application areas for anticipation, including some in environmental
engineering, are described to illustrate the possible use of these
techniques .
Key Words: Computer-aided design, computer graphics,
interactive graphics, remote graphics terminals.
1. An Engineering Problem
There has been much discussion the past few years concerning the use of graphical displays
attached to supporting computer systems. The load placed on such systems by highly interactive
display usage has demanded a large percentage of central system resources and has led to the use of
local logic and in some cases small computers associated with displays to relieve this burden from the
central system [1], [2], [3]. ^
It is desirable to have access to large computer systems which have large, high-speed main
memory, powerful instruction repertoires, and large backup file systems. The nature of the inter-
active activity associated with display usage is such that these powerful resources are required only
for short periods at relatively infrequent intervals. It is, therefore, economically advantageous to
attach several display terminals to a large computer system and to control their operation with a time-
sharing executive.
Chief, Computer Systems Section.
Figures in brackets indicate the literature references at the end of this paper.
37
The problems involved in supporting a number of graphical displays are greater than for
supporting slower teletypewriter devices, and early systems have served only a few displays, along
with a much larger number of teletypewriters [4], [5]. The use of intermediary computers to assist
each display terminal or a group of terminals promises to increase the number of displays that can
be serviced by one large computer.
Problems that arise v/hen using a local display computer to drive either one or many displays
are accentuated when the local computer is located at a considerable distance from the central system.
When located near the central system it is assumed that a very high bandwidth communication line can
be established between the local computer and the central system. At longer distances this may not be
possible. Even when it is possible, the cost of doing so may be unbearably high.
It is desirable, then, to utilize a restricted bandwidth communication line to interconnect the
local and central systems. For instance, it would be convenient if successful operation could be
obtained utilizing a single voice -grade line with a capacity of bits per second.
The limitations imposed on system operation with such a restricted line are immediately
obvious, since the nature of the data transmitted to and from the display is such that large amounts of
data are involved in the transfer of a complete picture. A picture with elements, each requiring
20 to 50 bits per element, requires 20, 000 to 50, 000 bits. With a single line, 8 to 20 seconds
would be required for transmission of a complete picture. If pictures are frequently required, this
time interval is too great for satisfactory man-machine interaction at the graphical terminal.
The question of what is done locally versus what is done at the central system acquires a new
meaning with a restricted communication line. The possibility of transmitting parts of pictures and
assembling them locally looks more appealing. Means for compressing data on the communication
line may also be useful, and any additional techniques that can be developed to enhance user response
time or system performance for graphical applications are of interest. The justification for a local
display-driving computer, rather than a buffer plus some simple editing logic, is even greater than
for displays adjacent to the central system.
It appears desirable to maintain an image of the general data structure stored in the central
system with a smaller, simpler one in the local system. Changes initiated by the display user can
thus be used to update the local image and immediately change the displayed picture as well as to
update the complete data structure in the central system at the same time. Minor changes made by
a display applications program in the central system to the complete data structure may be trans-
mitted incrementally to change the appropriate portion of the simplified local display structure. The
changes are immediately incorporated in the displayed image. Only when major changes are made to
the central data structure is it necessary to recreate from scratch the complete local structure. It
is only at such times that long delays will be experienced when using a restricted communication line.
One simple means for imaging a complex data structure is useful when an over-all picture is
composed of sub-pictures and perhaps mioltiple levels of sub-pictures. The basic sub-picture
elements can be stored locally and the composition of these sub-pictures into display images can be
directed from the central system. Sub-pictures, such as schematic representations of coils, fans,
and diffusers, may be identified by a short code and given a position for each "instance" in the dis-
played picture. It is unnecessary to transmit the detailed display generation information for each
sub-picture every time that sub-picture is used.
Despite use of such techniques, there will still be times when entirely new pictures are to be
transmitted or when such a sub-picture strategy is not useful. At times, a lengthy delay in responding
to a user's request may be inevitable. At other times, however, the technique described in this
paper, anticipating a user's needs, may be employed to minimize this delay.
2. The Anticipation Concept
Although several systems utilize anticipatory methods in one way or another, to the author's
knowledge there has not been a general exposition of these methods as a whole. Various anticipatory
techniques can be unified and applied in general to remote computer graphics. In some cases, use of
anticipation can lead to substantially improved terminal operation.
38
The concept is essentially the prediction of a remote terminal user's needs and the preloading
of programs and/or data that he may soon require. If, at any giv6n point in a user's interaction with
a system, the number of alternatives for major display changes are minimal and the probability of
choosing one or a few of these alternatives is high, then it is possible to anticipate his needs. While
the user is performing local interaction, or when the terminal is idle while the user is thinking, the
local computer can request one of the high probability pictures or programs. The request can be
transmitted and the requested pictures returned via the communication line, which is normally idle
during this interval between direct central system requests on the part of the user.
One example of anticipation has already been given. The prestoring of sub-pictures locally
in preparation for their assembly into complete pictures is the anticipation of the use of these parts of
larger pictures. Transmitting them to the local processor before they are needed makes the trans-
mission of full pictures shorter, and can decrease the over-all system response time to a user's
request which requires such transmission.
Another example of anticipation is the pre-loading of an entire set of programs and data for a
local computer from a central system in preparation for a particvilar application or class of appli-
cations. It has been suggested that for each application the larger computer could assemble a
package of programs for the local computer that will enable it to operate as independently as possible
and to require minimal service from the central system.
In both of these examples the success of the anticipation is dependent on the high probability
of usage of the pre-loaded programs and data. It is assumed that if a user requests an air distribution
system design program, for instance, then he will make use of this program, and therefore use the
prestored component sub-pictures, before calling another program having a different set of components.
It is likewise assumed that once a user has called for an application program, or has designated an
application class, that he will then be working in this application area for a reasonable period before
switching to another one. He may, however, have made a mistake; or he may change his mind. So
the proability of using the pre-loaded programs and data is not unity.
In general, anticipation is successful when the estimated probability of using data or a program
is sufficiently high. For any given collection of data and programs stored in the central computer
system, there is a probability of usage in the near future associated with each item in the collection.
There must be adequate local storage for that activity requiring immediate attention by the local
computer. To take advantage of anticipation, there must be some additional storage for data and
programs of slightly lower usage probability. If this storage is large enough to hold the entire
collection, then the need for central system storage is eliminated. This extreme represents a
substantial local investment and will not usually be practical. It is for a local storage size larger
than a few items, but less than adequate for the entire collection that it is useful to anticipate.
When the probability of need for an item is unity, it shall be considered essential for
immediate display terminal operation. If the item is not located locally, it must be requested from
the central computer system, and the user must wait for transmission of the request to the central
system and for receipt of the requested item. The usage probabilities of all presently loaded items,
data and programs, the probabilities of needing items still located in the central system, and the
amount of unused local storage must all be considered in determining possible anticipatory requests
by the local computer to the central system.
A request should not be made unless there is an item not located locally that has a high near-
future usage probability. The communication line must not be needed for direct activity in support
of immediate display operation. Storage must be available for the item locally. In some cases,
items may reside in local storage that are not needed immediately and which have a near-future
usage probability lower than these that can be requested. This space may be considered reclaimable
for high probability items as they are received.
Depending on the response time of the central computer to anticipatory requests, it may be
desirable to have several requests pending simultaneously. If a probability indicator is attached to
such requests, the central system might give them appropriate priority. Since assigned probabilities
are relative, it is possible for the probability of a requested item to change after the request has been
sent to the central system because of continuing display-user interaction. Depending on the system,
it may be desirable, if a significant change occurs, to send an addendum request or even an entirely
new request to change the priority given to the previous request. To do this, the local computer
39
should keep a list of pending requests. One important instance of such a change is if the probability
of an item changes from moderately high to unity, i. e. , it is immediately needed. If it has already
been requested, and if the central system does not vary service based on priority, then the local
computer just waits' for the reply. If priority is adjustable, then it might ask the central system to
increase the priority of the prior request or might submit a new, high priority request.
The notion of priority in submitting and servicing anticipatory requests can be extended to
take into account more than just the expected probability of usage in the near future. It can also
include some measure of estimated size of items being requested, thereby considering transmission
and service delay in obtaining the item and local storage that will be consumed by it after it is
received. These delays may be a function of current central system and communication line loading,
which might be measured by the local computer dynamically by noting the response times from the
central system. These times may vary according to type as well as length of requested items. All
of these considerations may be included in the priority- determining algorithms used for submitting
anticipatory requests as well as by the central system in servicing requests.
If the prime objective of system design is to optimize the display/user interface, taking into
accoiint the limited communication line, but not caring about the burden placed on it or on the central
system, then the primary concern in anticipating is to make sure the various system resources are
available for the highest probability requests when they occur, even if this means abandoning lower
priority requests in progress. Under some conditions, the added burden on the central system of
servicing anticipatory requests may be enough to limit the rate of input of such requests and may be
used to limit the generation of these requests by the local computer.
With respect to the communication line from the remote terminal to the central system, two
kinds of configurations may be considered: a dedicated line and a shared line.
3. Anticipation with a Dedicated Communication Line
If a single communication line connects the display terminal with the central system, then
conflicts of line usage may be resolved in favor of optimum user service. This selfish operation on
the part of the local computer may have to be tempered when central system loading requirements
are taken into account.
The nature of typical interaction between terminal and central system is such that the communi-
cation line is used normally only in bursts and is idle during relatively long intervals between bursts.
Here is a major system resource going unused- -a situation which can be used to advantage in some
cases by anticipatory techniques.
The resultant higher average usage of the communication line must not disturb the unity
probability item requests. Items needed before man/terminal interaction can continue must be given
highest priority. One way of accomplishing this is to give the local computer control over the communi-
cation line in such a way that it can interrupt transmission in either direction. This would ensure that
high priority messages are transmitted immediately. Another mechanism is to assign priorities to
requests and to ensure that all transmissions on the communication line are short. Short transmissions
can be achieved by selecting short message formats or by segmenting longer messages. In either case,
a highest priority message would be guaranteed of having the line within the maximum transmission
time of a short message or message segment. Highest priority transmissions in both directions need
not be as short as lower probability transmissions.
For the dedicated line the average usage should be higher than without anticipation, and there
will be some increased load on the central system to service the additional anticipatory requests.
4. Anticipation with a Shared Communication Line
Several graphical display users may share a communication line, either by mviltiplexing
through a corfimon local display-driving computer or through a communications concentrator, even
though each has his own local computer. With such shared activity on the line the average usage
will likely be higher even without anticipation, so there may be less unused capacity for anticipatory
use.
40
The same techniques for message priorities, inter ruptable low-priority messages or short
message segments, will allow highest priority requests to take over the line. With the shared line,
however, the effect of the low bandwidth line can be more evident if high priority requests are made
by two display terminals simultaneously. While in the worst case for one terminal a delay of 5 to 10
seconds might occur, this would double to 10 or 20 seconds with just two terminals. Of course, the
probability of exactly simxiltaneous requests is low, and the probability of worst case occurrence is
usually low with shared line usage.
Sharing of a communications line is a means for increasing the average utilization of an
expensive resource. Since effective anticipation thrives on unused resources, it does not do as well
as the load on the line becomes heavier. The same effect is evident as low priority anticipatory
requests compete for central system service. It is necessary to give higher priority requests from
all commiinication lines better service; otherwise, the system could be saturated servicing a large
number of requests that really should be given only unused central system resources.
5. Potential Applications
A few application areas appear very likely for the use of anticipation techniques. It is not
expected that all work in these particular application areas can benefit from these techniques, but
anticipation is a tool to be used as appropriate.
Suppose a user is scanning a large drawing, the entire detail of which is stored in the central
system. He observes the drawing, and may modify it, by looking through a "window" at some part
of the complete picture. In general, the greater the magnification, the more detail shown in the
window and the less area of the full picture that can be observed at one time.
Also assume that the local storage is adequate for what is currently being shown in the window
and for the necessary programs to manipulate it and to communicate with the central system. In
addition, suppose that some additional local storage is available, but not enough to store the entire
picture with full detail.
The user is scanning the over-all picture. This process consists of a combination of scanning
horizontally and vertically at a given magnification as well as switching to other magnifications as
needed. Suppose that a user has been observing a particular area for some time and that no prior
history is available to predict what he might do next. Equal probability may be given all sides of the
window- -unless it is at or near an edge of the over-all picture. It is possible to assemble those
picture elements just outside the window in a band as shown in figure 1. The elements in this pre-
dictor band are at the same magnification as the current window. Thus, if the user starts moving
in one direction, say to the right, the anticipation program can immediately handle movement the
width of the predictor band without communication with the central system.
Once such movement has been initiated, however, the local computer must request additional
picture elements to fill out a new band surrounding the current window. It may be desirable, depending
on user scan speed, available storage, and nearness to the over-all picture's edge, to bias the
anticipation band in the direction of movement, as shown in figure 2. When scan movement slows or
halts, estimated probabilities for movement in each direction based on the last and possibly earlier
movements can be used to determine any desired predictor band bias.
The operation of combining part of the predictor band with the present window during the
scanning process may be difficult. The effect of scissoring at the window edge, of viewing parts of
individual display elements, must be maintained as the window moves over the picture. A similar
problem exists on the opposite window boundary, where display elements or parts of elements must
be removed from the window.
This anticipatory scan at one magnification level may improve system response to the user.
It will not be adequate, however, if frequent magnification changes are requested. If the probability
of changing magnification is high, and if particular zoom levels are more probable than others, all or
part of windows at these levels may be anticipated and stored locally. If both single and multi-level
magnification scanning is possible and likely, then the anticipation routines must take both into
account--perhaps doing so dynamically depending on the user's operation. For the first few minutes
of a session the anticipatory routines can either use prior data for this user or use some universal
initial parameters. The anticipator can, thus, be made to adapt to particular conditions. It can
41
directly sense how well it is doing, since it can measure response times apparent to the user and can
adjust anticipation parameters to optimize some measure of response time.
Another potential application of anticipation is for scanning text. Such text might be
descriptive notes associated with working drawings within an interactive graphics application or it
could stand alone as separate documentation. Scrolling up or down continuous text is an operation
similar to, but simpler, than the full graphics scanning described above. Figure 3 shows a pre-
dictor band above and below a window of viewed text. Each band might include several lines of text
and variable predictor band bias can be applied as above once scrolling has begun.
The boundary problem is much simpler, since lines of text can appear and disappear as entities
without disturbing the window presentation. Structural text, that is, text having a hierarchial
structure with respect to detail, can be anticipated in a manner similar to that used for multiple
magnification levels, as described above.
Figure 4 shows the possible use of multiple predictor bands for text in various stages of
preparation for viewing. Those lines in band A might be ready for immediate viewing, while those in
band B are being retrieved from the central system.
Other potential application areas for anticipation include information retrieval from a highly
structured data base and browsing through a collection of documents. If the retrieval process is
gradual, such as working down a tree while narrowing in on an area of interest, then nodes may be
reached at which one or more branches have a very high probability of selection compared to the
others at that node. Especially in the case when selection of a likely branch requires substantial
transmission to the display terminal, anticipation coiild lead to considerably improved average
response times.
These few potential applications of anticipatory techniques will hopefiilly suggest many others
for which anticipation can be a valuable tool for improving system response. While looking forward to
the day in which high bandwidth communications lines will be widely available, this paper proposes
some ideas as to how to live with reality for some time to come. Even as such communications
capability is realized, the cost of a high capacity line will still be higher than a low one, and system
design trade offs will take into account the difference at any point in time.
6. References
[1] W.S. Barlett, K.J. Busch, M. L. Flynn, and Machine Communication," I.E.E.E. Trans-
R. L. Salmon, "SIGHT, a Satellite Interactive actions on Systems Science and Cybernetics,
Graphic Terminal," Proc. ACM June , p. 47.
National Conference, p. 499.
[4] F. J. Corbato, M. M. Daggett, and R. C. Daley,
[2] D.E. RippyandD. E. Humphries, "MAGIC-- "An Experimental Time -Sharing System, "
A Machine for Automatic Graphics Interface F. J. C. C. , Vol. 21, p. 335().
to a Computer, " Proc. F. J. C. C. , Vol. 27,
p. 819(). [5] Schwartz, J. I., Coffman, C. , and Weiss man,
C. , "A General- Purpose Time-Sharing
[3] J.E. Ward, "Systems Engineering Problems System," Proc. S. J. C. C. , Vol. 25, p. 397
in Computer-Driven CRT Displays for Man- ().
42
Window
Predictor Band
Figure 1. Uniform Predictor Band
Window
Direction of
Movement
Predictor Band
Figure 2. Biased Predictor Band
43
Figure 3. Text Anticipation
44
Computer Graphic Data Structures for Building Design
Marshall D. Abrams
Center for Computer Sciences and Technology-
National Bureau of Standards
Washington, D. C.
The data structures employed in computer graphics are
studied with the objective of discovering the common aspects of
structures now in use. A general graphic data structure is developed
for its educational value and employed to represent simple display
items. The use of list processing languages is discussed; an example
of a special-purpose structure is given
Key Words: Data structure, computer graphics, list
processing, pointers, hash coding, subpicture,
associative memory, multi-level storage.
1. Introduction
"Computer graphics" is the general term applied to th-e use of a digital computer to form an
internal model representation of an externally perceived graphical entity. The objective of such
modeling is to extract information from the graphical entity so that it may be modified, manipulated,
or otherwise processed.
After graphical information has been digitized, an organization must be provided for the
storage and retrieval of this data within the memory of the computer system. The linear array is
the simplest scheme available, but it is not of interest within the scope of this report even though it
enjoys wide use in certain classes of applications. Rather, this report will be directed to a dis-
cussion of those organizations which represent the relationships among the components of the
graphical entity. The relationships which must be represented within this subset of computer
graphics include topology and dependency relationships. It is most convenient to represent such
information in a hierarchical data structure which, in some abstract way, models the external
graphical entity.
Historically, this subset has been restricted to the study of line drawings, but gray-scale and
color representations are currently under investigation. The purpose of the data structure is to
facilitate the extraction of intelligence and manipulation of both the image and the information it
represents.
A graphical image is a preferred medium of human communication because of the possibilities
inherent for maximum information transfer with minimum effort. Graphical communication is often
highly stylized, requiring significant training for both the generation and interpretation of images.
Conventions are established and propagated through architectural education, which enable precise
communication with a minimum effort and non- graphical information.
Since graphical communication among humans is such an easy and effective technique, effort
has been expended to extend this communication to digital systems. As with other languages which
are clase to human language and far from machine language, considerable resources must be allocated
to store and manipulate the graphical communication within the digital system.
45
2. Overview of Graphical Data Structures
Both medium and conventions present difficulties associated with the digital representation
of graphical information. The significant attribute of the medium problem is dimensionality.
Graphics deals with two dimensions, often representing three dimensions. High speed primary
memory is usually addressed in a piece-wise linear fashion, therefore a transformation is required
to map the graphical structure into a one -dimensional frame. The information describing a graphical
entity must be stored in such a way that it can be retrieved, manipulated, edited, and used to produce
the desired graphical image.
The pertinent information associated with a graphical entity frequently consists of the geo-
metrical description of the graphical item: scaling, position, and orientation data; relationships and
connections to other items; name and identification of the item; graphical constraints on the item
itself and on its relationship to other items; and non-display (textual) data intimately connected with
the graphical entity.
One of the first decisions to be made in designing a graphical data structure is whether it
should be completely general, or tailored to a specific application. The general fixed structure
format is usually inefficient of storage since it must provide for unused options ^ [1]. Furthermore,
no matter how general the fixed structure was designed to be, there always exists the pathological
case which exceeds the capability of the structure. In such a case, one has no choice but to redesign
the structure, hopefiilly maintaining upward compatibility.
The tailored structure meets all of these objections, but necessitate the effort of construction.
In fact, the existence of general-purpose structures is extremely helpful to the user interested in
tailoring a structure to his application. The intellectual effort implicit in the general structure may
simply be transferred to the tailored structure, simiiltaneously modifying the structure to meet the
current objectives. Since most graphical data structures are pointer-type structures, with such
pointers being explicit or associatively addressed, the presence of a language designed to work with
such pointers greatly facilitates the construction of a data structure.
While it is certainly possible to build the entire graphical data structure up from scratch, the
use of a list processing or associative processing language greatly simplifies the work. In fact, most
of the literature ostensibly devoted to computer-aided design is in fact concerned with data structure.
Particular attention is called to references [1], [2], [3], [9] and [11] where the salient features of new
and more established "service" languages are discussed.
The next problem to be considered involves the communication of data to and from the
graphical data structure. This data will often be involved in the process of drawing a picture, in
modifying an existing picture, or in re-drawing a picture from the data structure. The use of
computer graphics in facilitating the convenient use of computers requires that this inf o rination trans-
feral process not be a burden on the human user [25]. Delay that is annoying to the user should be
avoided; a measure of tolerable delay is the user's concept of the difficulty of the task. While the
design of graphical processors is not within the scope of this survey, one cannot ignore the hardware
requirements forced by the desire for rapid response.
The mode of operation is for the user to communicate his desires to the digital system, often
using graphical input devices such as light pen, joystick, and mouse; and for the system to respond by
displaying the desired picture on his CRT display. Simiiltaneously the data structure needs to be
updated to reflect the changes resultant from the CRT activity. Rapid response criteria require that
at least part of the data structure must be instantaneously accessible to the user at the terminal [5],
[6]. The size of the local processor and the capacity of the communication line with the main system
determine the extent of the local image of the complete data structure.
A final problem is concerned with storage capacity in both the display driving computer and
in the central system. The portion of the data structure represented in the local memory is usually
less than that stored in the central system and may reasonably be restricted to that portion of the
structure being displayed. If additional storage is available, this may be augmented by logically
adjacent substructures possibly selected by an anticipator mode algorithm.
Figures in brackets indicates the literature references at the end of this paper.
46
Storage restrictions in the central system require greater attention and careful study. At the
time that a structure is created or modified, it is necessary that the storage used not be the limitation
upon the process. Thus, high speed core storage is required. Considering the possible extent of
graphical data structures and the core use limitations imposed by the operating system environment,
it is quite reasonable to expect and provide for the possibility of insufficient core storage being avail-
able. The solution exists in the form of a paging scheme, but careful attention and re -examination
must be paid to the design and handling of the paging [1[, [2], [3], [IZ].
3. General Graphic Data Structure
The concepts and techniques of graphical data structures will be introduced here in the form
of an example structure. This structure will purposely be kept at a level comprehendable to human
users and modifiable by them. It is not intended that this presentation be exhaustive, but rather
typical and hopefully educational. The organization of the data structure presented here is an
explicit referencing structure, similar to that of Cotton and Greatorex [5], the GRAPHIC- Z system
[4], [7] and GRASP [8]. The structure is certainly not exclusive; additional examples are given the
surveys by Gray [9] and Dodd [21]. The structure will be presented in the form of a directed graph;
the mechanism of representing such a structure in a computer memory will be discussed sub-
sequently.
In an effort to minimize the amount of graphics terminal machine language programming
required, especially by users that are not interested in such a level of detail, the commonly used
picture -building elements are provided as building blocks called "basic subpictures" . A basic sub-
picture may be a single command to draw (display) a point, line, or conic section; it may also be a
sequence of such commands to draw a commonly used geometric entity. Such basic subpictures are
often in the form of the "frame" or "skeleton" of an open subroutine, because the essential positioning
information must be supplied by each reference to (use of) the basic subpicture. The basic subpicture
data block must also contain the identification and relative location of the externally accessible
terminals of the subpicture, such terminals being the parts of points of connection to the subpicture
by the greater, outside world. If there are to be constraints on the use of the basic subpicture, these
constraints must also be contained within a block pointed to by the basic subpicture data block.
Within the context of basic subpictures lie all of the characters and geometric figures
directly presentable with a single machine level command, these constitute the "hardware character
set". Commonly used graphical entities may also be coded in graphical control language as a short
program, and provided as a time-saving service. Such basic subpictures provided might include
walls, pipes, conduits, doors, windows, etc. In addition it is desirable for a user to be able to
define his own subpictures which are useful for his application. The definition of a subpicture is
usually not within the scope of the graphical language -data structure being herein described, but is
at the level of graphical control language.
Thus, a picture is the highest level, encompassing all lower constituent levels. These lower
levels being collectively referred to as subpictures. The lowest level is termed a basic subpicture
in that it is the only level which references the display.
Using graph terminology, each basic subpicture is a node in the directed graph which is the
graphical data structure. Although it is quite possible for the node block to be of variable size,
herein pointers will be used to reference variable sized data segment blocks. Under these conventions,
a basic subpicture node can appear as in figure 1.
Since a basic subpicture does not possess any absolute frame of reference, it cannot in and by
itself cause any display. It must be referenced by a higher node to be used as a display item. These
higher nodes will in general reference multiple lower nodes, thus building a picture out of previously
created components. The terms "higher" and "lower" relate only to position in a directed graph
drawn to describe the structure and might instead be termed "subsequent" and "prior" respectively.
The construction of a picture is described by a directed graph wherein the top node is the
picture, the intermediate nodes are subpictures, and the terminal nodes are the basic subpicture.
A sample graphical data structure is represented in figure Z.
47
While it is fairly obvious that when expressed in computer code the picture and subpicture
nodes need to be represented by data blocks, it may not be immediately clear that the same is true
for the branches connecting the nodes. There is of course a trade-off between the information
associated with the node block and that associated with the branch block. The following selections
are somewhat arbitrary although typical [7]. The subpicture node block will essentially consist of
pointers to other information containing blocks. Among these blocks is the branch block, wh'ich
deserves special mention.
The branch block contains the necessary transformation on the lower nodes to incorporate
them into the subpicture defined by the subpicture node. Certain blanks in the skeleton frame of the
lower level picture must be completed, and other parameters may require systematic modification.
The transformation information consists essentially of displacement, scale, and rotation information.
Since all nodes except the highest "picture" node are intrinsicly referenced to zero, a new
reference displacement must be provided for each instance of use of subpicture and basic subpicture
node. This displacement may occur in a virtual display space having no size relationship to the
display viewing area; therefore, an additional displacement calculation may be required in the
process of display generation when the segment of the structure is selected for display.
Scale and rotation information must also be provided when constructing the present sub-
picture out of lower level items. In most applications it is unlikely that the rotation information will
require changing after picture -gene ration time, but scale may be a continuously varying parameter.
The analogy of photographic enlargement is accomplished by a modification of the scale parameter.
In certain applications this operation could be the critical item in operation of the facility. This
technique was first introduced as "homogenious coordinates" in Sketchpad [26],
The connectivity of the subpicture constituting the present level subpicture must be separately
treated. It is not sufficient to build a picture by appropriately placing subpictures so that their
terminals coincide. Subsequent parameter change in the branch blocks, or minor malfunction in the
hardware, could easily destroy such coincidence. Thus, there must be explicit provision for an
ordered relationship among the terminals of subpictures associated within a higher level picture.
For this reason, another block is provided, this being the "connector" block. The connector
block is a specific example of a constraint. It is presented as a separate block by virtue of its
prevalence. The connector block must identify the lower level terminals to be connected, and it
must point to the constraints on such connection. These constraints might include a requirement for
coincidence. If the terminals being connected were not coincident, the connector block would be
required to provide a line to form the connection. This line in turn could have attributes such as
intensity and rate of blink. These blocks may be represented by figures 3, 4, 5 and 6.
The design of the pointer scheme is a critical part of any data structure. An excellent dis-
cussion is given by Dodd [21], to which the reader is referred. The most simple pointer structure
is the single linked list wherein each block contains a pointer to the succeeding block in the list. The
pointer field in the terminal block contains a special symbol known as the "null pointer" indicating
the termination of the list.
The major shortcoming of the single linked list is the inability to return to the head of the
list without having previously saved the location of this head in a well known location to which
reference might be made.
The single linked list is rarely employed simply because a ring structure may be obtained by
having the end of the list point back to the head. Of course, the head and tail must be suitably flagged
to avoid endless ring-chasing. Another way of returning to the head of the list is to use a doubly-
linked list possessing a backward as well as a forward pointer, but this involves twice as many
pointers. It is, on the average, twice as fast as the single linked list in returning to the head of the
list.
Since the purpose of rings or doubly-linked lists is to be able to return to the head of the list,
or the list pointer, when a success or failure has occurred, the second pointer which the doubly-
linked list requires is often replaced by a back pointer to the head of the list. To conserve space,
the pointer to the head of the list may not occur in every block, but rather in strategically placed
blocks. Such a scheme is similar to, but simpler than, the CORAL structure [9], [13], [14], [21].
No common name exists for this pointer scheme. It is suggested that it be called a "pie" structure,
based on the diagram of figure 7.
48
A great deal of effort has gone into the development of pointer arrangements, this being the
critical decision in designing a data structure. The structures examined by Gray [9] appear more
different than similar, yet they are all concerned with related problems.
4. Constraints
One of the most important valuable aspects of the data structure for building design application
is the utilization of constraints. As has been mentioned, the terminal block is a form of constraint.
Additional constraints particular to this application are perpendicularity of planar surfaces and
inclusion of subpictures. The perpendicularity constraint assures that as subpictures are manipulated
that they retain the desired form. It is not sufficient to draw such perpendicularity without also con-
straining the data structure to preserve it under transformation.
Another valuable constraint is inclusion of one subpicture within another. By constraining
windows, doors, pipes and electrical services to remain within a wall it is possible to move the
wall during the design process and assure that loose ends are not left dangling.
5. Associative Addressing
The pointers used in the sample structure above are "explicit" pointers in that they address
direct access media [21]. For large classes of problems wherein the data base is subject to random
access, and is possibly stored in multiple levels of secondary and primary memory, content
addressability offers certain advantages. The essence of content-addressable, or associative,
memory is that it does not employ explicit addresses. A stored item is addressed by a partial
description of its contents. Current implementations [1], [2], [3], [15] are accomplished by soft-
ware, there being serious problems with hardware associative memories [1].
Interactive processors in general, and interactive graphics in particular, can benefit from the
use of associative languages. The programming techniques possibly may require a re-orientation
on the part of the user, but the poptolarity of associative language is attested to by several sources
[1], [3]. In part, the decision to use an explicit pointer or associative pointer language depends on
the availability, support, ease of utilization, and prevailing attitude at the installation where the user
is to work. The only a priori advantage of associative processing seems to be in the area of utilization
of secondary storage, which is discussed below.
6. Calculated Addressing
Since hardware associative memories have not economically arrived, associative systems
are currently implemented using a calculated addressing mechanism [1], Calculated addresses are
not restricted to schemes which explicitly involve content addressability, but even when they do not,
the underlying concept remains the same: namely, that the address of the memory location to be
accessed is determined by an algorithmic operation upon the contents of the pointer. In this usage,
the pointer is more aptly termed a "key" which may be part of information content of the data
structure rather than a separate item devoted strictly to pointing. Calculated addressing works by
treating the symbolic information as a set of numeric items which are to be manipulated by a known
and well-defined algorithm to produce a memory location address [1], [21], [22]; such an operation is
often called "hash coding".
One of the disadvantages of hash coding is that the calc\ilated address is not necessarily
unique. When two keys are calculated to point to the same memory location an ambiguity, or
collision, occurs. To provide for the advent of collisions, the pointer-chasing mechanism must
check that the contents of the calculated address matches the key used to calculate that address.
One strategy is to treat the contents of the calculated address as a pointer, usually a direct address
pointer, to a location within a block area where all the collision items may be found. It is perhaps
safest if a disjoint area is reserved for this purpose.
49
7. Multiple Levels of Data Structure Storage
The requirements *of fast response to operationally complex requirements and possible large
data structures necessitate that the structure be simultaneously maintained in more than one level of
storage, at least in part. First, consider the question of storage in the display.
Early graphical displays required the exclusive service of a large computer system. Today
the trend is to provide a small computer as the local service to each display and to service this local
processor-graphical terminal from the central system only when necessary. There is a whole
spectrum of capabilities of local processor attached to graphical processors. We shall not go into
the evolution of such dedicated processors here; the situation has been stated elsewhere [16]. Need-
less to say, however, the extent and kind of representation of the graphical data structure in the local
computer is highly dependent upon the kind(s) and amount of storage available, the instruction
repertoire, and the speed of the local processor.
The minimum information to be kept in the local processor is the display list which directly
controls the picture presented. The display list is extremely machine -dependent, containing the
necessary machine instructions to generate the display. If the computing capability of the local
processor is non-existent or extremely minimal it may be necessary to construct the display list in
the main system for transmission to the graphical display. In such a case the local processor fulfills
only the function of refreshing. In this situation it is impossible to reference the graphical data
structure via the display image because the display list has been generated only for display purposes.
In systems with minimum local processing ability, or even in more substantial systems, it
seems a waste of an expensive resource to store the display list in randomly addressable core
storage. It appears a better allocation of resources to use rotating storage for the display list. Not
only does this free core storage for programs, but it makes it possible to carry on display refresh as
a parallel process. Recent [17], [18], [19] and not so recent systems [20] have used this approa ch2.
The next step is to provide an association between the display list and the graphical data
structure. Such an association requires a referencing technique from the display list back to the
data structure. A pointer scheme can be implemented, but difficulty occurs as to the subpicture
level to be pointed to. Under various conditions the user at the graphical terminal might be
interested in pointing to a picture, a level of subpicture, or a basic subpicture. An automatic safe
technique is to have the pointer go to the highest level of subpicture being referenced, with the user
being able to initiate pointer chasing under his control to reach the desired lower level.
If memory and speed allow, part or all of the graphic data structure may be contained in the
local processor. If sufficiently large and fast, the local processor could contain the entire data
structure, generate its own display list, and reference the main system only for archival purpose or
for linking to other subsystems. In this form of operation the graphical subsystem can be considered
a "sketchpad" on which various trial drawings are made. When an acceptable one is produced it can
be preserved by referring it to the central computer.
In general, the data structure will be too vast to be contained completely in the graphical
terminal. A compromise is then effected wherein part of the data structure might be transported as
needed between the central system and the graphical subsystem. The degree of compromise is a
function of the processing capability of the graphical terminal, a subject well discussed by Myer and
Sutherland [16]. For convenient operation the transmission must occur within the user's wait
tolerance. When only part of the data structure is resident in the graphical subsystem, extreme
care must be taken with the pointer to the non-resident parts of the structure. There must be a
mechanism for flagging references to non-resident items; there must be a mechanism for enlarging
or contracting the size of the portion of the data structure available. These problems are quite akin
to the multiple -level storage problem in the central system, which shall be discussed next.
But a cycling display carries with it three prices to pay: (1) it is usually slow to access,
(2) it is fixed in size (but the size can be very large), and (3) it can be quite difficult to
respond to light pen interactions.
50
The adage of "a picture being worth a thousand words" is magnified in computer representation.
It can easily require many thousand words to store a moderately complex picture. Such storage
requirements can easily consume available high-speed primary memory.
It is certainly possible to design the driving and service program, the "resident system", into
minimally- interacting modules. These modules can be brought into core as pages [1] or overlays [12],
thus reducing the core storage which must be devoted to the system.
For user-created programs and data structures the situation is different. It is desirable that
as few restrictions as necessary be placed on the programmer. Therefore, systems are written which
automatically assign program and data to storage pages [1], [3], [12]. However, there is not total
rigidity in these page assignments; variable-sized pages [1] and partial user control [3] helps to adapt
the system to its current use. For the storage of the graphical data structures it is even more
important that the system be given as much information as is available. With complete information it
is possible to implement valid anticipation of program needs [3].
8. Sample Use of General Graphic Data Structure
Representing a graphical data structure on paper is an awkward necessity; awkward because
the confines of standard paper size makes it an exercise in topological ingenuity on the part of the
writer and parallax error elimination on the part of the reader; necessary because the expository
approach alone generally produces an incomplete information transferal.
The first illustration, in figure 8, is of the structure representing a triangle. This is a
trivially simple structure involving only one node and one basic subpicture. The one node, which is
automatically the top (picture) node points to three rings: branch, terminal, and connector. Each
block in the branch ring contains a pointer to the basic subpicture used, namely "point", the X, Y
coordinates of the instance of that point, and a pointer to the next branch block and back to the node
block. Each terminal block contains the coordinates of the terminal relative to the origin of the sub-
picture (which in this case are selected to be all the verticies), and the forward ring pointer. Each
connector block contains a pair of pointers to the terminals being connected, and the forward ring
pointer. All of the remaining fields contain zeroes interpreted as null pointers. The organization
of the blocks is in conformance with figures 1, 3, 4, 5, and 6.
Let us now use this triangle as a subpicture in building a larger picture. As an example,
consider the hexagon shown in figure 9(a). The triangle used of the subpicture is assumed to have
been drawn in the position shown in figure 9(b). Note that external terminals are denoted by small
circles in these figures.
The data structure of the hexagon is drawn in figure 10. Included is the terminal block ring
of the triangle data structure which is necessarily referenced by the connector ring of the hexagon.
Note the dotted lines representing pointers from the connector ring of the hexagon to the terminal
ring of the triangle.
These dotted lines from connector blocks to terminal blocks associated with another node
block are representations of an amazingly complex pointer chasing mechanism required. The
connector block must point to the branch ring which it accesses by pointing to the branch pointer in
the node block. From the appropriate branch block it obtains a pointer to the node block of the sub-
picture references. Also from the branch block it obtains the displacement, rotation, and scale
data which is necessary for the calculation of location of the desired terminal in the particiilar
instance of use. From the node block pointed to by the branch block it obtains the pointer to the
terminal ring associated with that level of subpicture. Finally, that terminal ring is traversed until
the particular terminal desired has been acquired.
Since such pointer chasing is not an abnormality in graphic data structures, there must be a
mechanism easing such constructions. The pointer concatenation facility of [23], recently
implemented by R. A. Siegler in conversational form as CL6 [24], is one technique which facilitates
such pointer chasing.
51
9. The Tailored Graphical Data Structure
As discussed in the overview, it is frequently convenient to construct a data structure which
is tailored to the graphical image to be modeled. The tailored structure can eliminate those features
of the general graphic data structure which do not apply to the problem at hand. The structure of the
graphical entity may be taken into account in designing the tailored structure; conditions which were
provided for in the general case may not occur. Therefore, the space reserved for the eventualities
in the general structure could be released for other use in a tailored structure.
Also as discussed in the overview, the use of a list processing language greatly simplifies the
work of creating a tailored data structure. Rather than continue with the abstract rendering of
geometric figures, the illustrative example of a tailored data structure will be concerned with compute
program flowcharts with which the author has been working.
10. Sample Tailored Graphical Data Structure
Our illustrative example will be a data structure used for the (internal) representation of
flowcharts. The data structure is created using the list processing language CL16 [24], a version of
Ij6 [23]. The defining portion of the program is exhibited as figure 11. Since the reader is most
probably not conversant in L^, the operations which are pertinent to the creation and use of the data
structure will be discussed in detail.
One useful feature in is the ability to define the location of a "field" within a "block" of
consecutive computer words. A field, once defined, may contain a pointer to another block, an
arithmetic value, or anything else the programmer desires. A field is designated by a single letter
name. The complete specification of a field includes the word in the block in which the field is to
exist, the name of the field, and the inclusive bit boundaries constituting the field within the computer
word.
The format of the field definition command is
( , D, , , )
where , , and are all integers indicating the relative work in
the block, and the inclusive bit botindaries within that word. < field name > is the single letter name
by which the field is symbolically referenced.
Like most programming languages, provides the programmer with a means for inserting
comment lines for internal documentation. In such comment lines must contain an asterisk in
column one and are ignored by the translator. In figure 11 the first six lines numbered 1 are
comment lines which explain the usage of the fields defined in line 0.
In the program, line 0 defines three fields in word zero: field I, the block number, bits 31
through 36; field B, the first forward pointer or message pointer, bits 1 through 15; and field C,
variously used as the back pointer, the input block pointer, or the count of the number of words in
the message, bits 16 through 30. The meaning attributed to field contents is the programmer's
responsibility. Note also that field definitions are non-unique, for line 4 defines field J to be bits 1
through 36 of word 0.
The ability to define those fields appropriate to the specific application is only one advantage
of the tailored data structure. It is used in this example to define fields in words 0 through 2 of the
block. Another advantage of this tailored data structure is the ability to define variable size blocks,
the size being determined during program execution. This feature permits optimum memory
utilization.
In L^, the procedure of defining a block is performed by the "get" operation having the
format
( , GT, )
52
where is the single letter, called a "bug", which points to and thereby identifies the
block, and is the number of words in the block which is being gotten.
In line 5 of the program, two fixed length blocks are obtained; block E being 3 words long and
block B being 65 words long. Skipping a few details, in line 12 a line of up to 65 characters is read
into B. This block is scanned for the end of line character, the carriage return, in lines 13 thtough 16,
keeping count of the number of characters in the line. In line 17 a new block D is gotten having length
C, where C was determined by the counting of lines 13 through 16. In essence, block B was used as
a fixed size input buffer from which the contents are transferred to the custom sized block D.
We could, if we chose, continue this detailed analysis of l6 as used for this application
program. The author does not believe that to do so would be of further educational benefit. Those
interested in following the workings of L;6 are referred to the defining paper by Knowlton [23].
In addition to the main pointer structure an auxiliary structure is provided. This auxiliary
structure consists of one word blocks, the fields of which are perforce identical to those of the zeroth
word of the main structure as shown in figure 12. This second string forms a linear chain most
easily searched and is only used for retrieving blocks in the main structure. This second string is
created on line 18 of figure 11. An example of the application of this structure is given in figure 13.
The flowchart segment represented is drawn in figure 14.
11. Refe:
[1] Feldman, J. A. and Rovner, P. D. , An ALGOL
Based Associative Language, Comm. ACM 12,
No. 8, 439-449 (Aug. ).
[2] Rovner, P. D. , and Feldman, J. A. , The
Leap Language and Data Structure, Proc.
IFIP Congress , C73-C77.
[3] Evans, D. and Van Dam, A., Data Structure
Programming System, op. cit. , C67-C72.
[4] Ninke, W.H. , A Satellite Display Console
System for a Multi-Access Central Computer,
op. cit. , E65-E71.
[5] Cotton, I. W. and Greatorex, F. S. , Data
Structures and Techniques for Remote Com-
puter Graphics, Fall Joint Computer
Conference, , 533-544.
[6] Kulsrud, H. D. , A General Purpose Graphic
Language, Comm. ACM, _H, No. 4, 247-
254 (April ).
[7] Christensen, C. , and Pinson, E. N. , Multi-
Function Graphics for a Large Computer
System, Fall Joint Computer Conference,
, 697-711.
[8] Thomas, E. M. , GRASP- -A Graphic Service
Program, Proc. ACM National Meeting,
, 395-402.
[9] Gray, J. C. , Compound Data Structure for
Computer Aided Design: A Survey, op. cit.,
355-365.
[10] Wexeblat, R. L. , and Free dman, H. A. ,
The MULTILANG On-line Programming
System, Spring Joint Computer Con-
ference, , 559-569.
[11] Van Dam, A., and Evans, D. A Compact
Data Structure for Storing, Retrieving,
and Manipiolating Line Drawings, op. cit. ,
601-610.
[12] Bobrow, D. G. , and Murphy, D. L. ,
Structure of a LISP System Using Two-
Level Storage, Comm. ACM, 10, No. 3,
155-159 (March ).
[13] Sutherland, W. R. , The On- Line Graphical
Specification of Computer Procedures,
Ph.D. Dissertation, M. I. T. (Jan. ).
[14] Kantrowitz, W. , CORAL Macros - -
Reference Guide, Lincoln Labs . ().
[15] Feldman, J. A., Aspects of As sociative
Processing, CFSTI AD 614-634 (April
).
[16] Myer, T. H. , and Sutherland, I.E., On
the Design of Display Processors, Cormn..
ACM, U_, No. 6, 410-414.
[17] Rippy, D.E., MAGIC U - Graphical
Display Terminal Interfaced to a Digital
Computer, Computer /Display Interface
Study, Final Report, AD (April
).
53
[18] Gear, C. W. , An Interactive Graphic Modeling
System, Dept. of Computer Science, Univ. of
ni. Report No. 318 (April ).
[19] Hostovsky, R. , Design of a Display Pro-
cessing Unit in a Multi- Terminal Environ-
ment, op. cit. , Report No. 343 (July ).
[20] Rippy, D.E., and Humphries, D.E., MAGIC-
A Machine for Automatic Graphics Interface
to a Computer, Fall Joint Computer Con-
ference, , 819.
[21] Dodd, G. G. , Elements of Data Management
Systems, Computing Surveys, J_ , No. 2,
117-133 (July ).
[22] Morris, R. , Scatter Storage Techniques,
Comm. ACM, 11, No. 1, 38-44 (Jan. ).
[23] Knowlton, K. C. , A Programmer's Descrip-
tion of l6. Comm. ACM, 9, No. 8
(Aug. ).
[24] Siegler, R. A, , The CL6 Conversational
List Processing System, Computer /Display
Interface Study, Final Report, AD
(April ).
[25] Miller, R. B. , Response Time in Man -
Computer Conversational Transactions,
Fall Joint Computer Conference, ,
267-277.
[26] Sutherland, I.E., SKETCHPAD: A Man-
Machine Graphical Communication System,
Spring Joint Computer Conference, .
FIGURE 2. SAMPLE GRAPHICAL DATA STRUCTURE
54
Identification as Connector Block
Pointers to Terminals
Blink Rate, Constraints
Pointer to Next Connector Block
Figure 3. Connector Block
Identification as Branch Block
Name of Branch
Pointer to Lower Node
Displacement, Rotation and Scale of Lower Node
Pointer to Non-display Information
Pointer to Next Branch Block
Figure 4. Branch Block
Identification as Node Block
Name of Node
Pointer to Terminal Block
Pointer to Branch Block
Pointer to Connector Block
Pointer to Non-display Information
Figure 5. Node Block
Identification as Terminal Block
Relative Location of Terminal
Pointer to Next Terminal Block
Figure 6. Terminal Block
BRANCH ma
POINT I
X| |Y| I 0 I 0
BRANCH BLOCK
POINT 2'
X2 I Y2 I 0 I T
BRANCH BLOCK
POINT 3
X3 I Y3 I 0 I O"
' POINT" DISPLAY LIST
NODE Bli3CK
•TRIANGLE"
BASIC SUBPICTURE
•• POINT'
TERMINAL BLOCK
0
0
TERMINAL BLOCK
h
TERMINAL BLOCK
Y2
TERMINAL BU3CK
"3
^3
CONNECTOR BLOCK
CONNECTOR BIflCK
0 0
CONNECTOR BLOCK
FIGURE 8. DATA STRUCTURE OF A TRIANGlf
(0.)
(b.l
FIGURE 9. HEXAGON, (o) COMPOSED FROM TRIANGLE, (b) TERMINALS DENOTED THUS: (^)
56
57
0 SETUPl :(0,D,C, 16,30)(0,D,B,1,15)(0,D,I,31,36)
1 * I z BLOCK NUMBER
I * B : FORWARD PR #1
1 * B = MESSAGE POINTER
1 * C = # WDS IN MESSAGE
1 * C : BACK PR
1 * C : INPUT BLOCK PR
1 : ( I ,D, A, 1 ,30) ( 1 ,D,D,31 ,36)
2 * A: BOX TYPE
2 * D : # FWRD PR
2 : (2,D,E, 1 , 15)(2,D,F,16,30)(2,D,G,31 ,36)
3 * E : FWRD PR # 2
3 * F : FWRD PR # 3
3 * G : # CHARS
3 : (3,0, H, 1,36)
A * H : ASCII WORD
A : (0,D, J, 1 ,36)
5 :(E,GT,3)(B,GT,65)(X,GT,4)
6 * X IS SUBR C
(6)
where
Ra
I exp (jwt)
m=o
The sign convention is such that negative values of load mean cooling loads and positive values
mean heating loads.
4.2 Lighting Sub-system
As in the thermal sub-system, clear day conditions are assumed for design. The analysis tackles
the inverse problem of determining the distance, D, from the window at which a prespecified level of
64
natural illumination, E , is available in the work plane and beyond which artificial lighting would be
required. A flux methSd similar to the lumen method {12} is used except that tabulated coefficients
of utilization cannot be used« in optimization studies. This problem is resolved by treating the
internal reflected component and the direct illumination from the sun and the clear sky separately.
The intensity of sunlight normal to the beam, E , the design diffuse illumination on a horizontal
surface from the clear sky, E^, and visible reflectances are specified for the problem.
Instead of considering it as a time-varying problem like the thermal sub-system, a design solar
altitude with respect to the horizon is fixed for lighting. This is a reasonable assumption, since it
has been shown by Hopkinson, Petherbridge, and Longmore {13} that for lighting in clear sky areas, where
reflected sunlight is very significant, the daylight and reflected sunlight components so adjust during
the working day that the sum of their contributions to internal lighting is practically constant.
To calculate natural lighting, the first step is to determine the amounts of direct and reflected
sunlight and skylight on any wall surface. The following equations have been used for the purpose:
= E^[ A + {B + C cos (a - a^)}"*"] (7)
E = E cos 6 cos (a - a ) (8)
oV n s
^SV = 0.5 R^.E Sin 9 (10)
(j n
^'^'1 = cos 1 {(sin 6 - sin L sin 0) / (cos L cos 9)} (12)
where E^ is the direct sky illumination, E^^ is the direct sunlight, is the ground-reflected
skylight, and is the ground-reflected sunlight, a is the bearing of the normal to the wall, is
the solar azimuth, 9 is the specified solar altitude, 6 is solar declination, L is the latitude of the
place, is the uniformly reflecting ground reflectance, and + means only positive values to be taken.
The reflections from neighboring facades have not been taken into account but direct sunlight has been
allowed for walls having (a-a ) less than 60 . For solar altitude of 30 , values of A,B,C are found
to be 0.40, 0.16 and 0.67 respectively for the clear sky {7}. These are based on computations by
Krochman {14}, and the values of E^ so computed are in good agreement with those recommended for
summer in the lES Lighting Handbook {12}.
The internal reflected component (I.R.C.) of natural illumination is computed by using the split-
flux principle {14} applied to clear sky conditions. The computation is oriented to an open plan
office so that the average internal reflectance is determined for the whole Internal surface area
under consideration. The actual component is determined for windows on each wall separately, and with
no constraints imposed by partition walls and no contributions from windows on other walls.
With these assumptions,
I.R.C. = T. K A^ [(VEsv> + ^V\SV^ \^ / ^13)
where T is the diffuse luminous transmittance of the windows (a design variable), K is the maintenance
and frame reduction factor, usually taken as equal to half, A is the total window area in any wall,
K is the floor reflectance, is the ceiling reflectance, A^ is the total internal surface area of
the building envelope, ceiling, and floor, and R^ is the area weighted average internal reflectance.
The required depth, D, is now obtained by solving the following transcendental equation by Newton
Raphson's method {15}
E = I.R.C. + T.KE ftan"! (^) - { (D) (H^+D^)"^} tan'^ { W(H^+D^ ) "^} 1 (14)
o w >• w J
where W is half the window width and H is the window height above the working plane.
From these values of D, one for each side, the area for artificial lighting is calculated. The
uniform luminance assumptions {13} implied in taking the bracketed expression in eq (14) are fairly
justified when reflected sunlight makes a dominant contribution to indoor lighting. It has not been
considered worthwhile to do more sophisticated lighting calculations for these optimization studies at
the present stage, but it may be done later at the detailed plan stage or when the groundwork and
procedure for the systems model proposed in this paper have been established in practice.
65
5.
System Design and Optimization
5.1 Design Problem Formulation
The environmental design of buildings has been formulated in terms of the independent systems design
variables P., as described in section 3. There are also dependent system variables, Q. such as the
ratio of luminous transmittance to the shading coefficient of windows, and total wall thickness, which
have to be considered in evolving practicable design solutions. As stated in section 1, the dependence
of external microclimate on design has not been considered in this model and is prespecified as input;
The response variables, R , such as indoor environmental temperature and daylight illumination determine
the performance level. Constraints are usually placed on the variables P. to satisfy the requirements
of bye-laws and the client's brief, on Q . to ensure practicality and economy, and on R^^ to satisfy
predefined environmental performance criteria. The mathematical formulation of the problem is as
follows :
Let P, Qj R be the column vectors defined by equations:
P =
{P.} ;
1
i =
1,2, m^
(15)
Q =
(Q.> ;
j =
1,2, m^
R =
k =
1,2, m^
where Q = Q (P)
R = R^ (P,Q,F)
- R (P)
for a given outdoor climate vector{F}and m^^, m^, m^ are the number of independent, dependent, and
response variables. If the lower and upper bounds vectors L and U be such that
{l}< (P, Q, R) <{u} (16)
where P, Q, R is the complete set consisting of vectors P, Q, and R, the design problem is to find a
vector P consistent with eq (16), which defines the feasible design space. Obviously, there are many
possible design solutions corresponding to the multitude of points enclosed in this space and in conven-
tional practice; only a very few intuitively selected alternatives are evaluated and one of these is
chosen.
5.2 System Optimization
The object of formulating a systems model and optimizing it is to select the best or near best of
an infinite number of possible designs without having to evaluate too many of them. First of all, an
objective function, S, has to be defined which is design dependent and is related to the merit of the
system. For environmental design, this may be minimum overall cost or minimum design cooling load for
satisfactory environmental performance when artificial control systems are available, or minimum degree
of discomfort for unconditioned buildings. The optimum design problem consists in selecting a vector,
P, so that S is optimized subject to eq (16).
The choice of optimization procedures is generally governed by the nature of the function S and the
constraint vectors L and U. The environment design problem formulated in sections 2 to 5.1 is a con-
strained optimization problem with a non-linear objective function and linear inequality constraints.
Also, it is desirable not to have to calculate the derivatives of the objective function to suit the
methods of analysis adopted. Further, the sensitivity of the optimum solution with respect to pertur-
bations in the design variables is more significant design information at the sketch plan stage rather
than the attainment of a global optimum. On account of these considerations, a sequential simplex type
search technique {16} has been selected. The search proceeds from an initial point, which may repre-
sent the best judgment for the values of design variables in the absence of optimization, or may be
generated pseudo-randomly in the feasible space. According to Mitchell and Kaplan {17}, a simplex of
points is generated around this initial point and the values of objective function are determined for
each of these points by a simulation program incorporating methods of analysis of section 4. The
optimization procedure continues through successive changes of the simplex position so that the worst
vertex is replaced by another one in a favorable direction {16} in any single move. The process is
continued until three successive changes do not modify the value of the objective function at the
simplex centroid by more than a desired amount governed by precision. The best point is obtained after
a specified number of such iterations, which use the best point from previous iteration as the initial
point for the next run. The result of optimization consists in the best value obtained for the
objective function, the corresponding optimum design solution comprising a set of values for the design
variables and the values of the objective function at the vertices of the simplex around this point.
66
It is to be noted, however, that the search methods do not guarantee the evolution of a global optimum.
In physical terms, the optimum design values correspond to the desired performance specifications,
and variations in the objective functions at the vertices indicate the sensitivity of this performance
to the largest permissible perturbations in the specifications, varied singly around the best design
solution.
6. Demonstration Example
As an example of application of the systems model formulated in sections 2 to 5, the top floor of a
multi-storeyed building located in Sydney (latitude 33.8 south, longitude 151.2 east) has been con-
sidered for optimization. The objective function has been chosen to be minimum peak cooling load
(sensible part only) for a typical climatic design cycle during summer {2}. Criteria for satisfactory
indoor environment specified that the indoor environmental temperature be maintained at the preferred
temperature for Sydney, 73 F with a2permissible rise of 3 deg F in the afternoons and an artificial
lighting intensity of 75 lumens ft to be available^on the horizontal work plane in all areas where the
design daylight intensity is less than 30 lumens ft
An open plan office is considered, with a central service core occupying 10 percent of the floor
area. The roof is designed to be a six layered structure with provisions for an acoustic ceiling, 1 ft
thick air space, 6 in concrete deck, insulation to be designed, waterproofing layer, and 2 in of concrete
topping. The floor is a similar structure except that there is a carpet instead of the three top
layers of insulation, waterproofing, and topping. The walls are specified to be rendered inside and
have three layers, two of which are design variables. The conditions of occupancy provide for 30
persons on each floor and a fresh air supply rate of three air changes per hour including infiltration.
Windows are considered to be provided on all four sides of the building, which is assumed to be located
on an exposed site. Nominal values of the other parameters which constitute the set of design
variables, and their upper and lower limits, are shown in Table 1.
Table 1. Input values for design variables of an open plan office building
Independent Design Variables (P.) Nominal Lower Upper
value limit limit
1
Wall, thickness of outer skin (in)
4.0
3.
,0
7.5
2
Wall, penetration coefficient of outer skin
(P*)
300.0
180,
,0
330.0
3
Wall, thickness of insulation (in)
1.0
0,
,01
2.0
4
Wall, penetration coefficient of insulation
(P*)
0.15
0.
,07
0.25
5
Roof, thickness of insulation (in)
3.0
2.
,0
5.0
6
Roof, penetration coefficient of insulation
(P*)
6.4
3.
,0
24.0
7
Roof, absorptivity
0.7
0,
,5
0.8
8
Wall, absorptivity
0.7
0,
,6
0.8
9
Window shading coefficient
0.5
0,
,4
0.6
10
Aspect ratio (north wall/east wall)
0.71
0,
,5
2.0
11
Window, light transmittance
0.1
0,
,1
0.8
12
Glazing ratio (glazed area/wall area)
0.5
0.
,3
0.6
13
Orientation (t^ue bearing)
082
082
082
14
Floor area (ft )
15
Ceiling height (ft)
9
9
9
Dependent Variables (Q^)
1
Wall thickness (P^^ + P^)
5.0
2,
,9
8.0
2
Window area/floor area
0.32
0.
,1
0.5
3
Light/heat ratio (Pj^^/Pg)
0.2
0.
,2
2.0
* p. Penetration_coef f icient = thermal conductivity x specification x density
(BTU in ft hr deg F)
The convergence criterion for the optimization program 'Design' is fixed so that if three conse-
cutively occurring design alternatives indicate peak cooling loads within 0.02 tons, the iteration is
terminated. Two such iterations have been provided for in the case of this example. The optimized
specifications and the sensitivity analysis are arrived at after about 150 design alternatives have
been examined by the computer. The CDC computer uses about 20 minutes of machine time for a com-
plete run of this type. Table 2 contains a set of optimized specifications and values for peak
cooling load ratios when each of the variables is successively put equal to the lower and upper limits
(Table 1), the others being kept fixed at the optimum level. The peak cooling load for initial
nominal design is 6.6 tons and it is reduced by 37 percent for the optimum design. Peak cooling load
67
ratios are the actual peak cooling loads divided by the value for optimum design.
Table 2. Optimization results for an open plan office building
Sensitivity analysis
T, c -c- ^- ^ ^- (Peak cooling load ratio)
No. Performance specifications Optimum
value , , „ -,
Value at lower Value at upper
limit limit
1
Wall, thermal resistance of outer skin
(R*)
0.56
1,
.02
0.98
2
Wall, penetration coefficient of outer
skin (P)
2.81
1
.00
1.00
3
Wall, thermal resistance of insulation
(R*)
0.89
1,
.01
1.00
Wall, penetration coefficient of
insulation (P)
0.15
1
.00
1.00
5
Roof, thermal resistance of insulation
(R*)
4.6
1
.06
0.98
6
Roof, penetration coefficient of
insulation (P)
6.25
0,
.99
1.04
7
Roof, absorptivity
0.6
0
.99
1.03
8
Wall, absorptivity
0.68
0,
.99
1.01
9
Window shading coefficient
0.53
0
.96
1.16
10
Aspect ratio (north wall/east wall)
l.Al
0
.99
1.00
11
Window, light transmittance
0.42
1
.00
1.00
12
Glazing ratio (glazed area/wall area)
0.57
1
.01
1.00
13
Orientation (tjue bearing)
Floor area (ft )
fixed
14
fixed
15
Ceiling height (ft)
fixed
* R = Thermal resistance = thickness/ thermal conductivity (ft hr degF Btu )
' 7. Acknowledgments
Thanks are extended to Mr. J.W. Spencer for help in the computer work and to Mr. E.R. Ballantyne
and Dr. R.W.R. Muncey for discussions. All computations were carried out on a CDC digital
computer which is part of CSIRO computer network.
8. References
{1} Gupta, C.L., A systematic approach to optimum
thermal design, ANZAAS Congress (Adelaide,
).
{2} Gupta, C.L. and Spencer, J.W., Building
design for optimum thermal performance, AIRAH
Jubilee Conference (Melbourne, ).
{3} Loudon, A.G., Summertime temperatures in
buildings without airconditioning , Building
Research Station, Garston, CP 47/68 ().
{4} Muncey, R.W. , The calculation of temperatures
inside buildings having variable external
conditions, Aust. J. Appl. Sci. 4_, 189 ().
{5} Muncey, R.W. and Spencer, J.W. , Calculations
of temperatures in buildings by the matrix
method: some particular cases, Bldg Sci. 3^,
227 ().
(6) Buchberg, H. , Sensitivity of the thermal
response of buildings to perturbations in the
climate, Bldg Sci. 4-, 43 ().
{7} Kittler, R. , Standardisation of outdoor con-
ditions for the calculation of daylight factor
with clear skies, in "Sunlight in Buildings".
CLE. Conference Proceedings, 273 ()
{8} Button, D.A. and Owens, P.G.T., Considerations
for the optimised fabric design, in "Engineer-
ing in the Home", 64 (Allen & Heath , ).
{9} Sheridan, N.R., Energy conservation applied to
the rational design of a dwelling for the
tropics. World Power Conference, Lausanne,
IV-B ().
{10} Vanning, J., Design of buildings to minimise
airconditioning loads, in "Airconditioning
System Design in Buildings", p. 72
(Elsevier, ).
{11} Hopkinson, R.G. and Longmore, J., Daylight,
artificial light and acoustics in relation to
the thermal environment, J. Instn Heat Vent.
Engrs 37_, 82 ().
{ 12} Illuminating Engineering Society, USA,
Lighting Handbook, p. 9-45 ().
{13} Hopkinson, R.G., Petherbridge, P. and
Longmore, J., Daylighting, p. 509 (Heinemann,
).
68
{14} Krochmann, J., The calculation of daylight
factor for clear sky conditions, in "Sunlight
in Buildings", CLE. Conference
Proceedings, 287 ().
{15} Lance, G.N., Numerical methods for high speed
computers, p. 128 (Iliffe & Sons, ).
(16) Kowallk, J., and Osborne, M.R., Methods for
unconstrained optimization problems, p. 24
(Elsevier, ).
{17} Mitchell, R.A. and Kaplan, J.L., Non-linear
constrained optimization by a non-random
complex method, J. Res. Natn Bur. Stand.
C72, 249 ().
Materials
and
components
Design
variables
Simulation
program
Indoor
environment
Compute
objective
function
System
simulation
System
optimization
Optimum
design
variables
Op t imum
as
initial point
Sensitivity
analysis
/ Optimized
j performance
specifications
End ^
Figure 1 - Building as an environmental system
69
Spatial envelope + internal components + external environment
+ heat sources
(Air temperature, degree of discomfort)/(plant capacity, loads)
Internal components
(Furniture and
partitions; areas
and types)
Spatial envelope + external environment
(Net rate of heat gain + radiant solar
heat gain)
Heat sources or sinks
(Mechanical services,
occupants, appliances)
E
^Air conditioning^
Spatial envelope + external
environment (Available
daylight - artificial lighting)
required
Spatial envelope
(Orientation, aspect ratio, ceiling height,
window area, surface absorptivities)
Elements of spatial envelope
e.g. wall (admittance, transfer ratio),
windows (shading coefficient)
Components of spatial envelope
e.g. wall outer skin
(Resistance and capacity)
Internal luminous
reflectances of elements
of spatial envelope
flight ing^
Materials of spatial envelope
(Penetration coefficient, P)
^ Thermal^
Figure 2 - Hierarchy for environmental performance simulation program
70
Design Considerations for a Practical Heat Gain Computer Code
Soren F. Nermann and Norman E. Mutka
DERAC Consultants, Inc.
Bothell, Washington
A digital computer program for heat gain computation is described. Einphasis
is placed on the development of engineering and programming design criteria to
ensure practicality, flexibility and ease of usage. Fenestrated and opaque sur-
faces, internal loading, plenum usage, duct losses, ventilation, et cetera are
considered. Computational questions are encountered which may form the basis
for future analysis and research. Results from the implemented code include the
determination of such design conditions as apparatus dew point, mixing and enter-
ing air temperatures, leaving and supply air temperatures, design and return air
quantities, number of air changes smd tonnage.
Key Words: Heat gain computation, design condition computation,
cooling load, apparatus dew point, air quantities, system design,
zone design.
1. Introduction
This paper describes the steps involved in the development of a particular digital computer pro-
gram to perform heat gain and resultant design condition computations. The program is structured to
be of value to the practicing engineer but is not a substitute for engineering experience and know-
ledge.
Evolved as a part-time project over a period of some three years, the program utilizes much of the
presently available knowledge, provides a framework wherein new developments may be quickly implemented
and has been thoroughly tested. There are, however, areas where it is felt additional research is
needed or where additional capability should be included. These areas form the basis for the future
evolution of the code.
2, Design Objectives
Before initiating any development of the code, the following design objectives were stipulated:
1) Engineering computations should include methods for the determination of:
a) fenestration heat gain.
b) wall or opaque surface heat gain.
c) internal heat gain.
d) plenum heat gain.
e) duct heat gains and losses.
f) ventilation and exhaust requirements.
g) leakage.
The computations should be valid at any site in either the northern or southern hemisphere.
2) The methods employed should be "standard practice" except where formulas might be developed
which would represent tabular data to some degree of accuracy in the least squares sense.
New developments should only be considered in unusual circumstances.
3) The code structure should be sufficiently flexible to permit the determination of the design
conditions within a zone or system given the applicability of any or all of the above heat
gain computations.
71
k) The input should be minimal consistent with the desires of the user for various capa-
bilities and should be structured to reduce the chances of error.
5) The results obtained from the code should be sufficiently detailed to permit hand
computation for checking purposes and to augment engineering experience.
6) The code structure should be sufficiently flexible to permit rapid changes, additions,
or deletions with a minimum of impact on the code, thereby enabling the code to keep
pace with new developments and techniques.
In addition a guideline was established whereby the criteria for selection between various methods
was practicality, i.e., if a particular technique was simpler or easier to implement and did not possess
any distinct advantage with respect to the final result obtained, then this technique was to be pre-
ferred.
3. Engineering Methods
Because of the number of algorithms employed to perform the engineering computations, only the
more significant techniques will be mentioned. A more detailed presentation will be found in
reference 8.
3.1 Preliminary Computation
The code employs the U.S. Standard Atmosphere, [?]''' to determine atmospheric pressure and
density at a given altitude. Solar data and sol-air temperatures are determined using the methods of
references 6 and 9.
Surface heat transfer film coefficients are determined from the following relations:
Internal film coefficient ['t]
= 0. cos^ T + 0.295^ cos T + 1.078 , (1)
-1 -2 -1
where H. is the internal film coefficient (Btu hr ft °F ) ,
1
T is the tilt angle of the surface (radians from vertical).
Elxternal opaque surface film coefficient [1,2]
H =2+4 W/15 (2)
e
—1 -2 -1
where is the external opaque surface film coefficient (Btu hr ft "F ) ,
W is the wind velocity (miles hr
External fenestration film coefficient [6]
= - 0. + 0.262 W + 1.45 , (3)
-1 -2 -1
where H is the external fenestration film coefficient (Btu hr ft "F ) ,
W is the wind velocity (miles hr ).
It will be noted that the selection with respect to the external opaque surface film coefficient
does not include a factor for surface roughness. On investigation it was found that the best avail-
able data for this coefficient [l,6] involved a subjective judgement on the part of the user which
■'■ Figures in brackets indicate the literature references at the end of this paper.
72
2
could cause wide variation in the determination of the coefficient . In addition the data did not cover
the full spectrum of today's surfaces. It is strongly recommended that future research be undertaken
which will more exactly quaintify this term.
3.2 Heat Gain Computation
3.2.1 Fenestrated Surfaces
Heat gain through a fenestrated surface is found from the relation
H = A |u(t -t.) + C[S^S^D,,(T^ + N A_ + N.A^ )
g g| oi ALND oD iD.
o a
+ D„(T, + N A, + N.A^ )] I , (h)
Id o d la.
o 1 '
where H^ is the fenestration heat gain (Btu hr
A is the fenestration area (ft ),
2 -1 -2 -1
U is the fenestration heat transmission coefficient (Btu hr ft °F ) ,
t^ is the outdoor dry full temperature (°F),
t^ is the indoor dry full temperature (°F),
C is a composite correction factor for haze, altitude, and internal shading [3]«
is a sash or frame correction factor,
S is the sunlit fraction of the fenestration area,
-1 -2
Dj^, are the direct amd diffuse incident solar intensity respectively (Btu hr f t ) ,
N , N. are the inward flowing fractions of the absorbed radiation through the outer
and inner panes respectively,
A A
D ' D. are the incident absorption coefficients for the outer and inner pames
respectively,
A A
d ' d. are the diffuse absorption coefficients for the outer and inner panes
0 1..,^
respectively,
Tjj, are the incident and diffuse transmission coefficients respectively.
The determination of the absorption and transmission coefficients is via a table look-up procedure
utilizing the data of reference 2.
The determination of the sunlit fraction of the fenestration area utilizes a generalization of the
procedure of Tseng-Yao Sun [9] to permit the use of tilted window surfaces. Adopting the same notation
as Sun, the shadow area depth is computed from the relation
ip _ ptanB-cosY cot6 ^ <
cosy+tanP cot 6 '
where T is the shadow area depth (in.),
P is the projection outward normal to the window surface (in.).
^ However, preliminary analysis of the data showed that two of the coefficients were related by the
relation
A = .004 C - . ,
and that the coefficient B might be related to the emissivity E by the expression
B = . e5- .
Here A, B, and C are as defined in reference 6.
73
3 is the solar altitude (radians),
Y is the wall-solar azimuth (radians),
6 is the counter-clockwise angle between the horizontal and the outward normal to the
surface (radians),
In addition provision has been incorporated in the code to eliminate the possibility of overlapped
shadow areas.
3.2.2 Opaque Surface Heat Gain
An extension of the method of H. A. Johnson [5] is utilized which enables application of the te
nique to heterogeneous structures. To make the extension, the homogeneous conditions postulated by
Johnson were approximated by computing "equivalent parameters" for specific heat, wall thickness,
thermal conductivity and specific weight as follows:
Specific heat
-I -1
(6)
Wall thickness
(7)
Thermal conductivity
(8)
Specific weight
H W.X.
1
/
(9)
where X. is the thickness of material i (ft),
W. is the specific weight of material i (lbs ft ),
-1 -1
C. is the specific heat of material i (Btu lb °F ),
•'- _]_ _]_ _]_
is the specific conductivity of material i (Btu ft hr °F ).
Hence the thermal diffusivity, A^, of the wall is given by
C W
e e
\ 1 ' 1
(10)
(x.A. )
1 1
The heat gain is then given by
H,., = A I D(T„ -T.) + H. T_ B cos(uu t-3 -6 ) , (11)
ID Si 1 — b n n n n I
' m n n
where A is the wall surface area (ft^),
D is the overall heat transfer coefficient (Btu ft hr °F "'"),
Tg is the mean sol-air temperature obtained from the Fourier analysis ("F),
m
T. is the room temperature (°F),
74
• • -2-1-1
is the interior air surface film transfer coefficient (Btu ft hr °F ) ,
T is the'n!!! Fourier coefficient (°F),
s '
i*)^ is the n«! harmonic frequency from the Fourier analysis (cycles hr ) ,
is the nU) harmonic phase angle from the Fourier analysis (radians),
n
t is the time measured from midnight (hr).
B and 6 are factors determined from the expressions
n n
B = d / Jf^ + i_ , (12)
n n / ' n n
6^ = tan"^(g /f ) , (13)
where
1 ^ e
f^ = a^ cosh T] cos ^ + ^ (sinh ^ cos r] + cosh r\ sin T])
+ a^ (sinh 11 cos r\ = cosh r] sin T)) , (15)
= cosh T\ cos 'H - ^ (sinh ti cos fl - cosh ri sin "P)
+ (sinh ri cos T) + cosh r\ sin t]) . (16)
Here
^n 4 J 2?r ' ^17)
o ^ e
o ^ e
n = x„ l-nn- . (19)
e
e
3. 2. 3 Internal Heat Gain
The internal heat gain is computed from the input sensible and latent heat data according to the
relation
h = Z d^.^M. • ^20)
1 11
where H^^ is the internal heat load (Btu hr ''■),
dy is the diversity factor for load i,
i
Hj^ is the maximum internal heat for load i.
i
75
3.2.4 Plenum Heat Gain
The code provides for the computation of heat gain from that portion of the internal load entering
the plenum directly and from the transfer of heat from either the space or through the exterior build-
ing structure. The impact of the air movement through the plenum is not accounted for at present.
3.2.5 Duct Heat Gain
Two methods are provided for the user. The first employs percentages of room sensible and room
latent loads to estimate the duct heat gains or losses. The second involves actual physical data con-
cerning the duct's construction and location as may be seen from the relation utilized to determine the
heat gain or loss, namely
h - "P^^^^^ 28.f;Vp!pX . (21)
where H_ is the duct heat gain (Btu hr ''") ,
-1 -1 -1
U is the heat transfer coefficient (Btu ft hr °F ) ,
P is the duct perimeter (ft),
X is the duct length (ft).
At is the temperature difference between the surrounding environment and the
air entering the duct (°r),
2
A is the cross sectional area of the duct (ft ) ,
V is the average duct air velocity (ft min ■*") ,
p is the density of the air (lbs ft .
3.2.6 Ventilation and Exhaust Requirements
Ventilation requirements are imposed via the relations
A is the amount of outside air required (cfm) ,
where 0
s
is
the
°L
is
the
A
is
the
t
0
is
the
t.
1
is
the
w
o
is
the
w.
1
is
the
0 = 1.08 A(t - t. ) , (22)
s o 1 '
0, = 0.68 A(w - w. ) , (23)
L o 1 '
Lr load (Btu hr "'') ,
, , -l^
door moisture content (grains lb-") ,
oor moisture content (grains lb-").
Utilizing this information as well as other information, an initial estimate is made of the return air
required. The air loads are then modified to reflect the percent (input) of the return air which is
to be exhausted.
3.2.7 Leakage
At the present time the amount of leaikage is specified as an infiltration quantity via input.
An extension to accommodate a more exact evaluation of this quantity based on crack length, door usage,
shaft and stack effects, et cetera, is under development.
76
3.3 Design Condition Computation
To determine the zone and system design conditions, the prograjm utilizes a mathematical formula-
tion whose exact structure is proprietary. However, because any such formulation must have an analog
with the more traditional graphical technique, it is convenient to describe the process in these terras.
Briefly, referring to figure 1, the apparatus dew point, T^, is found at the intersection of the
saturation curve with the effective sensible heat factor (ESHF) line, the mixture point is found at the
intersection of the grand sensible heat factor (GSHF) line with the line joining the indoor and outdoor
design points, and the supply air point is found at the intersection of the GSHF line with the room
sensible heat factor (RSHF) line. Note, however, that even under normal conditions the temperature of
the supply air, T^, will not be coincident with that of the leaving air, T^^, and hence a separate com-
putation for this point is included.
The program treats several abnormal conditions which may be categorized as follows:
a) T. - T > AT - the amount of sensible reheat is determined such that T. - T s AT
1 s max 1 s max
b) The ESHF line fails to intersect the saturation curve - a value of T^ is selected such
that T. - T s AT and the amount of reheat required is computed.
1 s max ^
c) The RSHF line fails to intersect the saturation curve - the amount of dehumidif ication
required to make the ESHF line tangent to the saturation curve is determined and then
if further refinement is required, the amount of reheat is computed so that
T. - T AT
1 s max
Obviously the above actions in response to the conditions mentioned will not satisfy all designers
but printout of the reheat sind dehumidif ication required will serve as an indication of the trouble
encountered. The designer can then take whatever action he considers best.
't. Program Structure
In order to meet the design objective of minimal input consistent with conditions and to provide
the maximum flexibility in use, modification, and extension, a modular approach was adopted not only
for the computational sequence but also for the input. To accomplish the latter a set of 25 key words
were defined which when coded on cards enable a structuring or blocking of the input stream. A parti-
cular block can then be included or omitted as conditions dictate. At the present time these words
are as follows:
Basic Data
TITLE
Titling information data block
ENVIRON
Exterior environment data block
DESIGN
Interior environment data block
ORIENT
Building orientation data block
GLASS
Fenestration data block
SASH
Sash data block
PROJECT
Window projection data block
MATERIAL
Building material data block
CONSTRUCT
Building construction data block
DUCT
Duct construction data block
DIVERSITY
Diversity schedule data block
77
Configuration Control
SYSTEM System definition block
ZONE Zone definition block
Space Data
AIR Outside air load data block
INTERN Space internal loads data block
WINDOW Window data block
BUILD Building surface data block
PLENUM Return plenum data block
RETURN Return duct data block
SUPPLY Supply duct data block
Execution Control
COMPUTE Initiate computation
UPDATE Data update or parametric analysis
NEXT Next building analysis
STOP Termination of computation
Referring now to figure 2 we see that after initialization the program scans for key words during
the input process, placing these key words and their associated data on auxiliary storage until a OM'UTE
card is encountered. This set of data forms the base line data case against which all subsequent up-
dating or parametric studies may be conducted. Since updating is accomplished dynamically during exe-
cution, the base line data case is preserved iintil a NEXT or STOP card is encountered.
It will also be noted in figure 1 that the input data stream is segregated into basic data, space
data and the two types of control functions permitting a preliminary scan of the data ordering to mini-
mize chances of computational failure. It will be further noted that the actual data input is accom-
plished via selection of a subroutine and its execution. Each subroutine reads and prints the input
data, performs whatever preliminary computation may be required and places the resulting data on
auxiliary storage.
Figure 5 shows the computational control sequence for the base line data case. The sequence is
designed to further ensure that the proper ordering of the input data has been accomplished. However,
it will be noted that it is possible to make a change in the basic data during execution of the case,
providing, for example, the capability to alter the interior design conditions within a particular
system or within a particular zone. Note also that the supply or return ducts require special treat-
ment, this treatment being necessitated by the fact that the data input for these data blocks may con-
tain percentages of room heat to determine the various heat gain or loss quantities.
The subroutines selected perform fenestration heat gain, opaque surface heat gain, plenum heat gain,
internal heat gain, et cetera. Following the determination and printout of the relevant heat gain con-
tributions, a table of the various sensible and latent heat factors is generated and printed for the
user's information. A design point is selected which reflects the maximiim heat gain and the design
conditions determined using a proprietary psychrometric process. Printout of these conditions is
given for each individual zone, if a multiple zone system, and for the total system.
78
5. Application
The program has been applied to a variety of structures, the following being typical:
A three story department store is located at h7.5° N. latitude, 122.3° W. longitude and at an
altitude of 300 feet above mean sea level. The building consists of a basement with an exposed loading
dock, a first floor sales area, and a second floor sales, stock, and office areas. The orienta-
tion of the structure is as shown in figure k. The construction is principally brick and concrete with
a single glass entrance shaded by an overhang.
The building was divided into four systems with the basement and first floor being treated as
single zoned systems SI and S2, respectively, and the second floor being treated as two multi-zoned
systems, S3 and Sk. Input to the program specified not only the location and orientation but the
weather conditions for the design day of August 21, the interior design condition of 7^°^ dry bulb and
62°F wet bulb, the detailed cross sections of the construction, the diversity schedules, and the inter-
nal peak load conditions. Duct factors, plenum conditions and required ventilation were also input as
required by the designer.
lypical of the output is that shown in figures 5 and 6 for system S2. Note that the various sensi-
ble and latent loads are given on an hourly basis. The design point occurred at 5:00 P.M. when the
maximum grand total heat was reached. Since the system was of the draw-through type, the mixture and
entering coil temperatures were the same. Note also that the difference between the supply air tempera-
ture and the space design temperature is less than the 23°F maximum difference which the designer
specified.
The results, in general, agreed with the hand computations, especially with respect to the compu-
tations pertinent to the psychrometric process where it is felt that the code produced a more reliable
result than the traditional graphical technique.
6. References
[l] ASHRAE Guide and Data Book - Fundamentals
sind equipment for and , George
Bantu Co., Menasha, Wisconsin, .
[2] ASHRAE Handbook of Fundamentals, 196?,
George Bantu Co. , Menasha, Wisconsin, 196?.
[3^ Carrier System Design Manual, Carrier Corp.,
Syracuse, New York, I96O.
[4] Hutchi nson, F. W, , A rational re-evaluation
of surface conductances for still air,
ASHRAE Transactions, 70 105 (196^).
[5] Johnson, Harold A., Periodic heat transfer
at the inner surface of a homogeneous wall,
ASHVE Transactions, 5ft 1^3 (19^+8).
[6] Lokmanhekim, Metin (ed.). Proposed procedure
for determining heating and cooling loads
for energy calculations - algorithms for
building heat transfer subroutines, (Prelim-
inary report by the task group on energy
requirements for heating and cooling, ASHRAE,
),
[7] National Aeronautics and Space Administration,
U.S. Standard Atmosphere, U.S. Government
Printing Office, Washington, D.C. , I962.
[8] Nermann, S. F. , COOL - A practical heat gain
computer code, DERAC Consultants document.
[9] Sun, Tseng-Yao, Shadow area equations for
window overhangs and side fins and their
application in computer calculations, ASHRAE
Transactions, 7^, I968.
[10] Threlkeld, J. L. , Thermal environmental
engineering, Prentice Hall, I962.
79
Figure 1
Typical Psychroraetric Process
80
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84
Output for System S2 Volume = IOO8OOO.OOO
System Design Conditions
Time of Peak Load I7OO Hours
Outdoor Dry Bulb Temperature = 83.000
Grand Total Heat = .000
Design Air (Variable Volume System) = 927^7.563
Return Air (Variable Volume System) = 7^7^+7.563
Design Air (Constant Volume System) = 927^*7. 553
Return Air (Constant Volume System) = 7^7^+7.563
Apparatus Dew Point Temperature = 5I.781
Mixture Temperature = 76.285
Entering Coil Temperature = 76.285
Leaving Coil Temperature = ^k.231
Supply Air Temperature = 56.1^9
Number of Air Changes Per Hour = 5.521
Tonnage = 216.1^3
Figure 6
System S2 Design Conditions
85
j
Solving the Communication Problem in
A Computer-Controlled Environmental System
T. Prickett, Jr., J. L. Seymour, Jr., D. L. Willson, and R. W. Haines
Collins Radio Company
Dallas, Texas
The use of computers in the control and supervision of environmental and other
systems for large buildings and complexes is just getting under way.
A fundamental problem in this type of application is the transmission of data
to and from the computer. The traditional methods of hardwiring, frequency multi-
plexing and electro-mechanical multiplexing are not satisfactory in a computer
environment, or in any complex, large-scale dynamic environment.
Both digital and analog data are needed in the control system. Digital data
can be handled faster and more accurately than analog data in both the communication
system and the computer. Analog-digital and digital-analog converters are needed,
with all information being transmitted in digital form. Then each data item becomes
a series of bits in a stream of digital bits, and can be transmitted over any type
of digital communication system.
This paper describes a communication system utilizing "time-division" in which
each discrete sensor and control element is assigned a unique time address in a
high-speed digital bit stream. By this means, the problem of addressing and communi-
cation is greatly simplified.
It is noted that this approach is made possible by the recent advances in micro-
circuit technology which makes it economically possible, for example, to use
individual A/D converters for each analog sensor.
The concept of approaching the "control problem" as a "communication problem"
should make it easier to analyze and design large computer-operated systems.
Key Words: Control, digital communication system, environmental system,
multiplexing, supervisory control, time-division address.
1. Introduction
There is a growing consideration of the use of computers for control of large and/or complex
systems, such as environmental systems in buildings or complexes. A few such systems have been
installed and others are being designed.
Central supervisory systems with or without computers become virtually essential for adequate
monitoring and control in large institutional or commercial complexes. They are justified economically
on the basis of improved visibility and control as well as reduction in personnel requirements and
lower operating costs.
The use of computers with supervisory systems increases the speed of data acquisition and
simplifies data reduction. If the computerized system is properly designed, much of the start-up,
shut-down and reset programming can be done automatically through computer-executed programs.
Since most large building complexes are dynamic and expandable the supervisory system must also be
dynamic and expandable.
A careful analysis of such systems indicates that a basic difficulty is the need to deal quickly,
accurately and efficiently with large quantities of data. For example, in a typical industrial complex
with 2,000,000 square feet of air-conditioned floor space, proper monitoring and control requires
87
communication with about sensor and control devices. Some of these must be monitored regularly,
others only intermittently.
This paper considers various traditional methods of data communication, and concludes that a
digital system using time-division addressing may be the best approach.
2. History of Supervisory Control Systems
Central supervisory controls for environmental systems are a comparatively recent development.
Design changes have been evolutionary, rather than revolutionary, dictated by the increasing size and
complexity of the buildings.
The first such systems were simply extensions of the control wiring (or piping) from a few systems
to a central point (fig. 1). Since separate, permanent connections are required for each control
function, this is usually termed a "hardwired" system. This approach is satisfactory so long as the
subsystems to be coordinated are few in number and closely related geographically.
As the number of subsystems increases and they become more widely separated, the cost and com-
plexity of the "hardwired" approach makes it necessary to look for alternatives. Multiplexing, in one
form or another, is such an alternative. The basic idea of multiplexing is to use a common bus or a
set of "common function" wires which serve all the subsystem control devices. Some means of
"addressing" is necessary to select each station in turn for monitoring and control operations. The
devices which perforin the addressing and selecting functions are called multiplexers (fig. 2). Multi-
plexers take various forms depending on the concept and the type of data being handled. The more
common forms are frequency multiplexing and electro-mechanical and solid state multiplexing.
The frequency multiplexer uses a set of discrete frequency carrier waves, one frequency for each
station to be addressed, on which the signals to be sent and received are superimposed. This is, of
course, subject to error due to variations in frequency or voltage at the power source, and extraneous
"noise" due to frequencies from other sources.
Another type of scheme uses a series of pulses as the carrier system. The number of pulses per
unit time, or the elapsed time between pulses can be varied to correspond with the signal value. These
pulse groups can be combined to form a continuous stream, with divisions between individual signals
indicated by some sort of a coding system.
Electro-mechanical and solid state multiplexers use relays which will, in response to a proper
address signal, connect the common function wires to the subsystem desired. This operates reliably,
but is comparatively slow.
The first central supervisory systems to use computers simply patched an analog computer into the
manual control board and used the computer for monitoring and data acquisition (fig. 3). It was obvious
from the beginning that the analog computer could also be used for control. However, the digital com-
puter is preferable for control purposes, although there are many software problems, including those
associated with multiplexing and demultiplexing.
3. The Nature of Control Data
Data in an environmental control system are both analog and digital in nature. Analog signals are
associated with temperature, humidity, flow, pressure and modulating position, while digital signals
are associated with two-position, on-off, start-stop, go-no go, and similar functions. If these data
are handled on a manual basis, as they are in most presently installed supervisory systems, then speed
is not important and data can be transmitted in either form. If, however, we wish to use a computer-
controlled communication system, then digital data should be used. Digital data can be transmitted at
much higher speeds, and with greater accuracy, than analog data. It then becomes necessary to provide
analog to digital (A/D) or digital to analog (D/A) converters for the analog-type sensors and con-
trollers; thus the communication system need handle only digital data.
Only a small amount of data is derived from any single function, and this can be handled at rates
as low as 120 bits per second (BPS) or less. The computer, however, operates at speeds up to several
million BPS. It is therefore necessary to provide hardware to make these bit speeds operate together.
One such system which is used is called time-division multiplexing.
4. Time-Division Multiplexing
Time-division multiplexing is defined by its name. A high-speed, repeated, digital bit stream is
generated by the computer and fed into the main communications bus (usually a coaxial cable). At each
device, or group of devices, a coupler is connected to the main bus in such a way that it interfaces
88
with a small portion of this bit stream (fig. 4). A typical "slice" is one word, and consists of the
same word each time. That is, the coupler is identified by a particular time segment (or slot) in the
repeated bit stream. Another word is identified with a second coupler and so on. In one system, the
bit rate of the coupler is bits per second. This is derived by repeating the 32-bit data word 150
times a second. The minimum bit rate required on the main bus is then BPS times the number of
couplers on the bus. The actual bus bit rate is usually greater than this minimum to provide for
buffering and synchronization.
In this system the coupler address is said to be "strapped," that is, a particular time slot is
permanently assigned to that coupler and the computer identifies the data as coming from that coupler
by its location in the repeated bit stream. Strapping is essentially a hardware function and is used to
reduce software. We noted earlier that most control devices require 120 BPS or less. Therefore, it is
not necessary to use a separate BPS coupler for each device. But we can serve several control
devices from this one coupler by using a secondary bus with low speed device connectors to reduce the
bit rate still farther (fig. 5). If these connectors are also strapped, no further addressing is
necessary.
Many control devices require regular monitoring and a permanently strapped connection. But some
devices may require only infrequent service and a permanent connection is not required. By assigning
a group of connectors to a larger group of devices and providing a "switching" program, these devices
can be connected (addressed) as required with a reduction in hardware, but with an increase in software
to take care of the switching. A certain amount of overhead is necessary to provide addressing, but it
is much less where part of the addressing capability is inherent in the hardware. Providing switching/
addressing routines in the operating programs increases the overhead and slows down the operation. A
trade-off study must be made in each case to determine the most economical method.
In a similar manner, a single A/D or D/A converter can be made to serve several devices by multi-
plexing techniques. This is feasible because these converters now operate at high speeds. It is
possible to provide a "free-running" A/D conversion system which continuously scans several analog
signals and stores the present values of those signals in a set of digital storage registers. The
computer operating program then provides for reading the contents of the registers at timed intervals.
While time-division multiplexing may be programmed into almost any general -purpose computer, it
would be very wasteful of software and storage capability. It is preferable and desirable to use a
computer system which has the time-division addressing and data handling included as part of the basic
hardware-software package. The operating programs then become much simpler to write and debug.
The operating program must be written for each specific application. However, this too can be
simplified by the use of a high-level language, such as ATLAS, which uses a fairly simple English
syntax and covers a broad spectrum of test and control functions. Of course, any high-level language
requires a compiler resident in the computer. This, in turn, implies a fairly large computer, but
greatly reduces the cost of the software, both for the original program and for changes and additions.
The time-division multiplex system thus described is made possible by the recent advances in
microcircuit technology, which allow the design of complex circuits in small packages and at low cost.
We expect to soon see most of the necessary hardware contained in small MOS/LSI chips at a cost of less
than $100 each. By using this approach, the computer is relieved of complex addressing operations and
is free to concentrate on the business of control.
5. Conclusion
We believe that the effectiveness of a computer-controlled system depends largely on fast and
efficient communication. A time-division multiplex system designed to be integral with the operating
computer system provides the best, simplest and most reliable communication available today. This
system also allows for connection by a simple coaxial cable, and is easy to expand, requiring only
additional interface hardware, extension of the coax bus, and small additions to the operating program
as more devices are added.
Appendix
Time-division addressing systems may be "bit-interlaced" or "word-interlaced." Figure 6 shows a
typical main bus "frame" for a bit-interlaced system. This contains 16 channels (bits) per frame, with
the first bit being amplitude-coded for synchronization. A coupler may be strapped to read one specific
bit (time slot) from each frame as in figure 7. When 36 frames have passed the coupler, 36 bits have
been extracted to form a complete word. (This number 36 is arbitrary, and varies to suit the manu-
facturer. A 36-bit word, as shown, provides four supervisory bits and 32 bits of data. The supervisory
bits identify the type of data being transmitted.)
89
Figure 8 shows a word-interlaced system, in which the coupler is strapped to identify and read one
specific word out of a frame which contains 256 words or channels. (Again, the number 256 is arbitrary.)
With either system, it can be seen that the time slot is identified with a specific coupler and
that all channels in the frame are serviced essentially simultaneously. Thus the system is ideal for
real-time, on-line control.
ROOM
TEMPERATURE
AIR HANDLING UNIT
SUPPLY
PRESSURE
WATER
TEMP
BURN I NG
MOTOR
PUMP
MOTOR
RETURN
WATER
TEMP
CENTRAL
CONTROL
PANEL
COMPRESSOR
MOTOR
SUPPLY
WATER
TEMP
©
PUMP
MOTOR
RETURN
WATER
TEMP
RETURN
WATER
TEMP
©
COOLING TOWER
©
PUMP
MOTOR
SUPPLY
WATER
TEMP
Figure 1. Hardwired Central Control
90
CENTRAL
CONTROL
PANEL
WITH MUX
COOL I NG
TOWER
Figure 2. Central Control with Mux
91
COMPUTER
CENTRAL
CONTROL
PANEL
WITH MUX
Figure 3. Central Control with Mux and Computer
92
PROCESSOR
PRIMARY COMMUNICATION BUS
COUPLER
2
SECONDARY BUS
COUPLER
N
TO
DEVICES
TO
DEVICES
TO
DEVICES
Figure 4. TDM Bus with Mux
DEVICE
COUPLER
PRIMARY BUS
SECONDARY BUS
ADAPTER
ADAPTER 2
■ADAPTER 3
ADAPTER N
Figure 5. Mux with Secondary Bus and Device Adapter
93
LI FRAME
13 14 15
12 3 4
10
13
16 BITS
16 CHANNELS (TIME SLOTS)
Figure 5. LI Frame Format
LI FRAME 0
0
LI FRAME
1
14
15
1
2
f
14
15
(
0
LI FRAME 35
2
0
1
1
SO
SI
S2
S3
0
31
DATA WORD FROM CHANNEL I
Figure 7. Channel/Data Word Relationship
TDM FRAME
WORD 252
WORD 253
WORD 254
WORD 2 55
27
28
29
30
31
COMMAND
* BITS "i
INFORMATION BITS
I WORD (TIME SLOT)
Figure 8. TDM Frame Format
94
A Linear Programming Model for Analyzing
Preliminary Design Criteria for Multizone
Air Distribution Systems
R. A. Gordon
Cornell, Howland, Hayes (t Merryfield
Engineers - Planners - Economists
Corvallis, Oregon
A linear programming model has been developed to analyze design
criteria affecting multizone air distribution systems and to provide
information for making design decisions during the preliminary, or
conceptual, phase of building design. The location of potential pri-
mary mechanical equipment spaces; physical constraints for the air
distribution systems; zone data, including preliminary air require-
ments and single-point zone distribution coordinates, and basic system
configurations are fed into an IBM computer to develop a mathemati-
cal model of the building multizone air distribution system. Linear
programming is then applied to determine the "least first cost" multizone
air distribution system. Postoptiraal reports are developed to show the
effects of price changes in the air distribution systems or primary
equipment selections, the physical size of mechanical equipment spaces,
and changes in zone requirements (and the ranges for which the effects
would be valid) on the least first cost system selection. Parametric
reports are also developed to show the effects of utilizing alternate
primary mechanical equipment spaces as well as other system changes in
which several variables are changed simultaneously. Examples of applica-
tions of linear programming in preliminary multizone system design situa-
tions are presented.
Key Words: Air conditioning systems, air distribution systems, equip-
ment selection, linear programming, mathematical programming, multi-
zone systems, optimization, postoptimal analysis.
1. Introduction
The conceptual development of design criteria affecting mechanical systems is a phase of building
design that must be reevaluated before optimal design of these systems can be accomplished. Computer-
aided design systems and new mathematical techniques offer designers new opportunities to optimize the
conceptual and ultimate final design and to provide additional tools for maintaining cost controls
over the project. The need for additional tools for analysis of mechanical system design criteria is
becoming of greater importance as the costs of building continue to rise and as the costs of the
mechanical system continue to consume an ever-increasing portion of the project budget.
In this paper, we will discuss an application of linear programming as a component of a design
system to assist in evaluating design criteria effecting a multizone air distribution system. Some
basic requirements for a system of this scope are: a data base permitting up-dating of the original
design criteria with a minimal amount of data m.anipulation by the designer, the ability to analyze
changes in design criteria in terms of effects on the total system and capability of providing the
results in the form required for the decision-making activities of the designer, performance of design
calculations, optimizing the design and, to some extent, estimating costs, material quantities and
equipment selection. All these must be accomplished with an economic advantage over the traditional
methods of the conceptual design.
95
2. Linear Programming
It is difficult to define the class of problems which linear programming can solve. In general,
these problems include a variety of different resources to be distributed in a variety of ways. A
number of constraints may be applied. Some or all of the items may be available in limited quantities,
or are tolerable only up to certain limits, or some may be parceled out only in integral units. Under
these constraints, an overall measure, such as cost or profit, is to be minimized or maximized.
*
For a precise formulation of the general linear programming problem L2J, we assume aj^^ , b^, and Cj
are sets of constants (i = 1, ...,m; j = 1, ...,n) and Xj (j = 1, . . . ,n) is a set of decision variables,
We seek solutions X = (x^, X2 , . . . ,Xjj) which satisfy the inequalities
I a^jX. > bi
j=l
i = 1,
,m
(1)
Xj >_ 0
1,
(2)
and at the same time minimize the linear functional
X = I c .X .
J J
j = 1
(3)
The linear programming problem is to obtain such a solution.
Equation (3) defines the objective function X and this function is linear in each set Xj . The
value of X is a function of the vector X = (x^, ''n^ ' ^^"^ hence we may express (3) as
X = f (x^, x^, ... ,x^) . (4)
The function is defined for all values of X with finite components; however, our consideration is
limited to those values whose components satisfy restrictions (1) and (2) .
We see that in eq (1), we require that the components satisfy m linear inequalities, and in eq (2),
we require that all components be non-negative. We commonly refer to eq (2) as the non-negativity
restrictions, and to the inequalities (1) as the functional constraints. In matrix terminology, we
may represent the functional constraints by the equation
A = X _> B (5)
in which A = (a^^j) aiid B = col (i) .
While the non-negativity restrictions merely limit the set of admissible vectors to vectors X with
positive or zero components, the functional constraints further limit this set to those vectors satis-
fying the matrix inequality (5). The restrictions and the functional X characterize that part of linear
programming in which we attempt to minimize an objective function.
The linear programming problem may be stated in an equivalent form in which a linear functional is
to be maximized and the functional constraints are >_ relations rather than <^ relations. Since this
problem is obtained from the one stated by multiplying eq (1) by -1 and minimizing -X, this case can be
covered adequately by discussions of the minimizing problem.
Number in the bracket refers to the reference.
96
3. Development of Preliminary Design Criteria
3.1 Assumptions
In the development of conceptual design system involving the application of linear programming as
a design tool, some initial ground rules must be defined. The reason for selecting the multizone
system out of all mechanical systems available is simply because data regarding packaged units are
readily available. Also, the distribution systems for each zone are much easier to identify and thus
lend themselves more readily to this type of a system solution.
Those portions of multizone air distribution system representing the primary cost variables are
used in this model. Supply registers and other hardware, will remain fairly constant in the basic
system configurations. However, the return and exhaust systems are actually separate systems somewhat
similar in scope to the supply distribution systems. As such, they could very easily be included as
additional elements of this same model. Their presence would lengthen this presentation so they have
been omitted. Other discrepancies resulting from the assumptions made so far can be partially ex-
plained since the design system being discussed is used to define conceptual design criteria. Hence,
only the variable cost factors that make it difficult to determine optimal system design are included.
3.2 Preliminary Design Criteria
Preliminary design computations are performed within the limitations of conceptual design criteria
through a series of subroutines described very briefly herein.
a. Air Volume Computation
In the early phases of design development, a method of estimating the cfm requirements for supply
zones, is required to establish realistic bounds for the mathematical model being developed.
The amount of ventilation air required is computed on the basis of any one of the following cri-
teria :
1. Number of air changes per hour,
2. Volume of air required per occupant,
3. Volume required per square foot of floor space.
first method, C = n x V : for the second, C = A x N: and for the third, C = B x S.
* V r V v
= volume of ventilation air flowing, cubic feet per hour.
= number of air changes per hour.
V = volume of the room in cubic feet,
r
A = cubic feet of air per hour per occupant.
N = the number of occupants.
B = air volume required per square foot of floor space.
S = the area of the floor in square feet.
The method selected and used depends upon the judgment of the designer.
b. Duct Sizing
After computation of the zone air volumes, we can determine the size of ducts that are required
to transport the air. The subroutine presently used for this purpose computes the equivalent duct
diameter using a constant friction loss of 0.1 inches w.g. per 100 feet of equivalent duct length for
air volumes less than cfm, and a constant velocity of feet per minute for air volumes in
excess of cfm.
For the
C
V
n
97
For the volume of air less than cfm, the equivalent duct diameter ClD is:
= (2.7(Q/250t)l-«2)l/l-^0
(6)
For Q greater than cfm,
D = (AQ/Vtt)-'-''^
(7)
In eqs (6) and (7) ,
= equivalent duct diameter, feet,
V = air velocity, feet per minute,
Q = air flow rate, cubic feet per minute.
The general form of the equation for conversion of the circular duct diameter to the equivalent
rectangular duct is :
d = 1.30(ab)°-"/(a+b)0-"0 , (8)
c
where
a = length of one side of rectangular duct, inches,
b = length of adjacent side of rectangular duct, inches,
and
d^ = circular equivalent of a rectangular duct for equal friction and capacity, inches.
In the conversion, it is necessary to consider both the aspect ratio and any space restrictions in
which the ducts are to be routed.
The aspect ratio (AR) is the ratio of the long side to the short side. An increase in the AR in-
creases both the installation cost and operating cost of the system. Therefore, it is desirable to
maintain an AR as near unity as practical. This is accomplished using the following algorithm.
For the case in which the aspect ratio is 1, let a = b in eq (8) and compute d . If d , as pre-
viously computed, is less than the limiting d , then set a = b and recompute 'a' us5ng the computed
value of d :
a = (1.46D )
c
1/2.375
(9)
If d^ is greater than the limiting value for d^, set be equal to the maximum depth and compute 'a'
Interpreting 'a' as the length of the longest dimension of the rectangular duct, the gage of gal-
vanzied steel required is then selected from Table 1.
Table 1. Galvanized steel sheet metal gage
for rectangular low pressure ducts ClU.
Dimension 'a'
Inches
Through 12
13 - 30
31 - 54
55 - 84
85 and greater
Gage
26
24
22
20
18
Lb/ft
0.906
1.156
1.406
1.656
2.156
98
This information is contained within the duct sizing subroutine so that all information about t
duct run required to make a cost analysis has been determined except for the length of duct run. The
method of obtaining the length of duct run for each zone is briefly described in the next section.
c. Spacial Description
Determination of lengths of duct runs is assumed to be based upon a single point of delivery to
each zone. In most projects during preliminary design, this assumption is presumed sufficient.
Similarly, assuming that the discharge plenum from the multizone units may also be adequately
described as a single point, it is easy to describe the multizone unit in the three dimensional space
Using the three dimensional coordinate system, the points of supply and distribution are then
uniquely described by sets of coordinates. By comparing coordinates, it is then a simple task to com
pute the length of ductwork from each zone to each multizone unit. With this final data, the cost pe
unit volume of air for the ductwork for all possible system configurations is easily obtainable.
d. Multizone Unit Costs
In Table 2, the incremental costs for multizone units are listed.
Table 2. Incremental costs for horizontal blow through, heating and cooling multi-
zone units with insulated coil and fan section, drain pan, forward curved
wheels, DWDI, Class 1, motor with vari-drive and belt guard and heating and
cooling zone
system of 2
: dampers , with
inches C43.
a coding
coil face velocity
of 550 fpm,
, and
ASU
No.
min
cf m
max
First
Cost
$
+80%
Total
Cost
$
min
$/cfm
ave
max
1
2,500
3,500
850
680
1,530
.612
.525
.437
2
3,500
4,500
1,000
800
1,800
.514
.457
.400
3
4,500
6,500
1,200
960
2,160
.480
.406
.332
4
6,500
8,800
1,420
1,136
2,556
.393
.342
.290
5
8,800
11,000
1,700
1,360
3,060
.347
.313
.278
6
11,000
14,000
2,080
1.664
3,744
.340
.303
.267
7
14,000
17,000
2,480
1,984
4,464
.318
.290
.262
8
17,000
21,000
3,000
2,400
5,400
.317
.287
.257
9
21,000
23,500
3,300
2,640
5,940
.282
.267
.252
10
23,500
30,000
3,970
3,176
7,146
.304
.271
.238
To determine the appropriate cost factors to use in the objective function of the LP model, the
cost per cfm of air volume for the recommended mtiximum cfm and the minimum cfm, are averaged. As
indicated in Table 2, these values include consideration for the installation costs.
e. Duct Costs
Table 3 represents the installed costs of galvanized sheet metal ductwork L4ll. The costs also
include the sheet metal contractor's profit.
To determine the total installed costs of low pressure, straight rectangular ducts on a lineal
foot basis , add the width in inches and the depth in inches and multiply by the appropriate multiplie
from Table 3.
99
Table 3. Cost factors for galvanized steel sheet metal for low pressure rectangular
ducts [Ia3.
Duct Gage Multiply by
26 0.140
24 0.162
22 0.195
20 0.217
18 0.234
To determine the cost per cfm for the duct from each multizone unit, the total cost is divided
by the volume of air being supplied. This figure is then used in the LP model in the objective
function.
4. Formulation of the Multizone LP Model
A linear programming model for multizone air distribution systems can now be developed from the
previous discussions. Given 'n' competing activities consisting of the volume of air required for
each zone, Zk, and the volume of air available from each source, ASUs , the decision variables
X. , X , . . . ,x , in (2), represent the levels of these activities. The general form of the model is
illustrated in figure 1.
In our model, the volume of air required for the k^'^ zone is formulated as
r
EZil.K = ZK k = 1, . . . ,p (10)
1 = 1
for a system with 'r' multizone units and 'p' zones.
Similarly, the volume of air supplied by the r'"'^ multizone unit is formulated as
r
TASUJl.s <_ TCAP s = 1, ...,t (11)
a = 1
where there are 't' possible selections for the r''^ multizone unit.
The summation of the individual zone air volume requirements supplied by a particular multizone
unit and the total capacity of the multizone units in the solution base must be zero, or
r p t
E (IZl.k. - lASVl.s) = 0 . (12)
1=1 k=l s=l
Furthermore, the volume of air supplied to each zone from a particular multizone unit must not
exceed the total volume of air required by the zone, or for the k zone,
ZH.k <_ Zk i = 1, ... ,v (13)
and each multizone unit cannot supply a volume of air in excess of ASUs, or for the s^^ multizone unit,
ASUil.s < ASUs 1 = 1 r . (14)
100
Finally, the objective function, COST, can now be written as
r p. t
Z (j:(CO)l,k) (Zi.k) + r(CAi^.s) (ASUi.s)) = min COST (15)
1=1 k«=l s=l
Since, by our previous discussions, each of the Zil.k and the ASU2..S are assumed linear over the range
for which they appear in the solution base, our model then performs according to the general linear
programming problem.
5. Results
The experimental values obtained during testing of the computer-aided design model thus far sub-
stantiate the possible economical use of the model in analyzing conceptual design criteria for multi-
zone air distribution systems.
A test building for which design data has been recorded, has been used to verify the results ob-
tained from the model. Typically, input data for 30 zones has required about one hour for prepara-
tion. Using an IBM computing system, about 15 minutes are required for computation of the bounds
for the LP model and the cost coefficients for the objective function. The LP model, using the IBM
LPMOSS C3ll program, requires about 30 minutes to obtain the first optional solution.
Output from the computer-aided design model includes the following:
1. The minimal possible first cost for the multizone air distribution system using
the given set of design criteria,
2. The determination of the multizone unit from which each zone must be supplied to
obtain the minimal system first cost,
3. The multizone unit selection for each subsystem required to minimize the first
costs ,
4. Cost per unit of air volume for all duct runs and multizone units in the range for
which the solution is applicable,
5. Cost reduction or increase possible per unit volume of air within the vicinity of
the optimal solution achieved by changes on the constraints.
After the initial optimal solution has been determined, the output data is extremely useful in indi-
cating the directions in which to proceed to improve upon the solution. This may be as simple as
changing one or two bounds, or as complicated as changing the location of multizone units or a number
of zones. The constraints are automatically modified, as well as the coefficients in the objective
function. Since the initial optimal solution is maintained by the program and used as the new initial
solution, the analysis of the new design criteria is accomplished in a substantially reduced time and
reduced design cost.
Additional modifications to the model will include printout of the optimal air distribution system
using a plotter, modeling of additional basic air distribution systems, the use of graphical display
devices, and the consideration of return and exhaust air systems.
101
6, References
ASHRAE Guide and Data Book, Systems and
Equipment. . ASHRAE, New York, N.Y.
936 p.
Hillier, Frederic S. and Gerald J. Lieberman.
. Introduction to operations research.
San Francisco, Holden-Day, Inc. 632 p.
[3] International Business Machines. .
Linear Programming - Mathematical Optimiza-
tion Subroutine System ( LP-MOSS) , Pro-
gram Reference Manual. White Plains, New
York; IBM.
C^D Richardson Engineering Services. . Man-
ual of Commercial and Industrial Construction
Estimating & Engineering Standards. Vol. I.
3 3
< <
3 3
C/3 CO
< <
<
O
O I-
< <
< <
102
A Conceptual Survey of Computer-oriented
Thermal Calculation Methods
C. L. Gupta , J. W. Spencer and R. W. R. Muncey
Commonwealth Scientific and Industrial Research Organization,
Melbourne, Australia
This paper surveys computer-oriented methods used for calculating cooling or
heating loads and/or for determining indoor space temperatures in buildings. The
methods have been classified into groups depending upon the way they tackle the
underlying heat conduction problem. Limitations and merits of each of these
techniques are then discussed in terms of the ease of computation and degree of
exactness with which they handle considerations such as heat conduction through
multilayer walls and roofs, heat capacity of the enclosing fabric and of the contents,
internal radiant loads and radiative-convective exchanges, ability to provide for
an internal temperature swing and thermostatic operation, variable ventilation,
shading, surface coefficients of heat transfer, and heat flow through the ground.
Harmonic or matrix methods and response factor methods are discussed in greater
detail.
Key Words: Air conditioning, computer, indoor climate, load calculation,
survey, thermal performance.
1. Introduction
The importance of designing buildings as
environment modifiers and the economic necessity
of accurately estimating the loads for correct
sizing of air conditioning devices has led to
considerable development of dynamic thermal
calculation methods. The advent of high speed
electronic computers has shifted the emphasis
from development of simplified handbook methods,
necessarily based on very restrictive assumptions,
towards making more routine use of sophisticated
methods already available and to develop more
exact ones. An ideal method should permit the
designer to know accurately how the thermal
performance or air conditioning loads on a
building vary with time of day and time of year
and the influence of variations in the building
structure, the control conditions within the
enclosed space, the capacity and operating
schedule of the plant, and the behaviour of the
sensing and thermostatic control devices.
The thermal environment of any confined
space is the result of interaction between the
outdoor climate, the enclosing structure and the
energy sources or sinks within. The commonly
required data for thermal calculations are design
climatic conditions, thermophysical properties of
the structure, heat inputs due to occupancy,
appliances, ventilation, and lighting, and the
desired indoor conditions required for comfort.
To obtain design climatic conditions, a selection
criterion is used to pick out time sequences for
external air temperatures, wind velocity and
solar radiation from meteorological records.
Alternatively, solar radiation can be computed
from an assumption of atmospheric conditions and
a knowledge of solar position. The selection
criterion is independent of thermal calculation
methods and has not been discussed in this paper.
It has to be noted, however, that simplified
handbook methods, which form the basis of the
majority of current computer programs in routine
use, do not permit as wide a selection of design
solar radiation values as they do for air
temperatures. Similarly, the design values for
internal heat input and thermal comfort conditions
are independent of the calculation method adopted,
even though they may be handled differently by
different methods.
In regard to heat flow through building
elements, most computer-oriented methods assume it
to be unidirectional and thus neglect corners and
heat bridges such as studs and rafters. The
thermal conductivity and heat capacity of
homogeneous layers are considered to be constant
even though their values may be taken with
reference to moisture conditions likely to occur
Division of Building Research
)
'Division of Forest Products
103
in use. Thus the governing differential equation
for heat conduction through a building element is
the one dimensional, linear heat conduction
equation. The corresponding simplification in
boundary conditions, obtained by neglecting the
non-linear character of surface coefficients of
heat transfer or by treating them as constant, is
no longer universally adopted. Air in the
enclosed space is still considered to be at a
uniform temperature and non-absorbing to
radiation.
2. Types of Thermal Calculation Problems
In the field of thermal design of buildings
and load estimation, four main types of problems
are encountered:
(a) Calculation of indoor air temperature in
the absence of artificial cooling or heating.
(b) Calculation of indoor air temperature when
some heat is being removed or added but the
indoor temperature is still variable.
(c) Calculation of heat gains or losses and
cooling or heating loads when the indoor
air temperature is kept constant at a
known value.
(d) Calculation of heat gains or losses and
cooling or heating loads when the indoor
air temperature is variable and specified -
the case of "temperature swing".
Further, the variable inputs may be of
periodic type or of any general type. The former
yield to exact steady periodic analyses and are
usually sufficiently representative of design
conditions but the latter are necessary when
energy usage is being considered over a large
period of time or actual comparisons are being
made in the field between observed and computed
values.
Significant concepts to be discussed in
relation to the various thermal calculation
problems are:
(a) Heat conduction through multilayer elements.
(b) Converting the solar radiation transmitted
through windows and the internal radiant
loads to cooling loads or changes in indoor
air temperature.
(c) The ability to handle variable networks
representing either a variable amount of
ventilation or variable coefficients of
heat transfer at the surfaces of walls
and roof.
(d) Automatic controls such as thermostatic
control of temperature and operation of
blinds.
(e) Interactions with daylighting, latent load
calculations, shading due to other
buildings, more complicated considerations
of multidimensional heat flow through heat
bridges and ground, and coupled heat and
mass transfer problems.
3. Established Design Methods
A limited comparison of the established
design load estimation methods, which form the
basis of most computer programs in current use,
has been carried out by Milbank and Harrington-
Lynn(l)^. A detailed discussion of the
mechanism of heat transfer in buildings has been
reported by Gupta(2). To provide a proper
perspective for the methods reported in later
sections of this paper, major concepts in relation
to three methods, which are widely used and
represent basically different approaches, are
discussed in this section.
The ASHRAE method (3) is limited to load
estimation for conditioned spaces held at constant
air temperature. Specified values of surface
coefficients of heat transfer are assumed in the
exact analytical treatment for steady periodic
flow, which forms the basis of determining the
equivalent temperature differences used in this
method. Heat conduction through multilayer
elements is treated rather empirically. Sol-air
temperature allows for the effect of solar
radiation on opaque elements and solar heat gain
factors and shading coefficients allow for the
amount of solar radiation entering through
windows of different types. Average clear days
are used for estimating solar radiation. The
instantaneous cooling load due to internal radiant
loads and transmitted solar radiation is obtained
by averaging these over a period of time governed
by the weight of the structure.
In the Carrier method(4), the equivalent
temperature differences for opaque elements are
calculated for sunlit as well as shaded conditions
by using numerical methods. The internal radiant
loads and transmitted solar radiation are
considered to be absorbed by the structure. Based
on field measurements, hourly storage factors are
tabulated, which when multiplied by the peak solar
heat gain through ordinary glass give hourly
cooling loads corresponding to different weights
of structure, different shading conditions and
different hours of plant operation. Allowance is
made for reduction in peak values of load for
different amounts of temperature swings permitted
in internal space temperatures. The incident
solar radiation values can be adjusted for a haze
factor.
The method due to Boeke(5) is widely used in
Scandinavian countries and seems to be very
general in its approach. It calculates loads for
a specified indoor air temperature which may be
constant or variable or else determines the indoor
'Figures in brackets indicate the literature references at the end of this paper.
104
air temperature for a given plant capacity and
also in the absence of artificial sources and
sinks. Computations on an hourly basis are done
for cycles of clear as well as cloudy days in
every month of the year by using hourly heat
balance equations for similar modules in the
building. The modules are supposed to have only
one wall exposed. Heat transmitted through
opaque portions, shaded as well as sunlit, are
calculated by using Carrier's tables (4).^ Internal
radiant loads and transmitted solar radiation
through windows are considered to be absorbed by
a hypothetical element representing the ceiling,
partitions and floor in a two lump system
corresponding to the core and surface. The
special features of the method are its capacity
to tackle variable shading due to other buildings,
variable ventilation, environmentally controlled
operation of blinds and lighting, thermostatic
control of indoor air temperatures and
intermittent plant operation in a straight
forward operation. The inaccuracies involved in
the handling of conduction through multilayered
slabs are of the same order as in other design
methods. The main limitation seems to be the
provision for only one exposed element.
There are many other proprietary programs
such as ARTHUR and BASIL in France, WESTINGHOUSE,
APEC and GATE in the USA. Also there are a large
number of easily programmable desk calculation
methods, using unsteady state heat flow
considerations, which are very widely used in the
USSR and European countries. By and large, these
do not use any significantly different concepts
and differ only in detail. A discussion of these
is omitted for lack of space.
For purely numerical methods, which form the
basis of digital computer programs of this type,
both space and time derivatives are converted into
finite differences. This results in a set of
algebraic equations which can be easily handled by
matrix algebra. In physical terms, this
approximation amounts to representing a distributed
thermal system by a lumped thermal network
consisting of resistances between nodes and
capacitances at the nodes and to calculating step
by step with respect to time. The larger the
number of lumps and steps, the nearer to the
actual system this representation would be but the
computer time required would be increased.
A vast body of literature(lO) exists for
numerical methods of solving the heat conduction
equation, but the following discussion should be
sufficient for outlining the concepts and defining
the terms.
The one dimensional heat conduction equation
for a homogeneous medium with constant thermal
properties is represented by
3^1 _ 1 8T
2 ~ a 3t (1)
3x
where T is the temperature, x is the space
dimension, t is the time and a is thermal
diffusivity. Considering h to be the incremental
step in x and e in time t and using the notation
T(m,n) to represent the temperature at position
mh at time ne, a general finite difference
representation of eq 1 would be
4. Numerical Methods
It is not always convenient to obtain exact
analytical solutions of the one-dimensional heat
conduction equation under the varied boundary
conditions of interest in building heat transfer
problems. In fact, it is not possible to obtain
these by purely analytical means if the boundary
conditions are non linear or thermal properties
become temperature or time dependent. Also, for
multilayered slabs, the exact number of layers
have to be specified in advance, thereby
restricting the generality of application. It is,
therefore, of interest to consider numerical
methods, which essentially involve the conversion
of derivatives into finite differences. If only
the space derivatives are converted, the equation
reduces to a set of simultaneous ordinary
differential equations at a grid of points or
nodes. These have been solved by using R-C
network analysers, analog computers and thermal
analysers, which require a specific type of
equipment and involve experimental errors. Large
size analogs, which can handle thermal problems
of buildings as a whole, have been reported in
recent literature by Korsgaard and Lund(6),
Button and Owens (7) and Euser(8). The basic
principles of these have been reviewed by
Stephenson(9) and these will not be discussed
further in the present paper.
&{r(m+l,n+l) -2 r(m,n+l) + T(m-l,n+l))
+ (1-6) (Tfm+l^n) -2 Tfm^n) + T(m-l,n))
J
T(m,n+1) - Km,n)
(2)
where M = aeh is the modulus and 6 is the
interpolation parameter. The relative magnitudes
of £ and h are to be chosen such that the scheme
is computationally stable, i.e. the rounding off
errors do not go on increasing and their actual
magnitudes govern the accuracy of finite
difference representation. The conditions of
stability(lO) are that
M > 0, if 0.5 $ 6 ^ 1
0 < M $ 0.5 if 6 = 0 (3)
If 6 = 1, an implicit form is obtained, which is
stable for all values of M. It involves solving
a set of simultaneous equations for every time
increment, which may, however, be large. If
6 = 0, an explicit form is obtained, which is
stable only for M ^ 0.5. This means that even
though only one equation has to be solved for
105
each time increment at each node, the increment
has to be very small, being necessarily less
than half the smallest time constant of all the
nodes for stability.
Two well known cases are obtained as follows:
If 6 = 0, M = 0.5, eq (3) becomes
(4)
T(m,n+1) =0.5 {T(m+l,n) + T(m-l,n)}
If B = 0.5, M > 0, eq (3) becomes
^{Ol(m+l,n+l) + Km+l,n)) - 2(J(m,n+l) + 1(m,n))
+ (.T(m-2,n+l) + T(m-l,n))} = Km,n+1) - T(m,n)
(5)
Equation (4) corresponds to Schmidt's method
and eq (5) corresponds to Crank-Nicholson's
method (quoted in 10). The former is simple but
accurate only up to second order differences and
can give oscillating errors if the initial
estimates are not chosen properly. The latter is
more accurate and is stable for all positive
values of M.
All numerical methods require initial values
to be specified and generate temperature data at
all nodes even when only air temperature and
surface temperatures are required. There are
also lumping errors due to nodal approximation of
a distributed network by a discrete system, which
can be made quite small at the cost of
considerable increase in computer time.
Nevertheless, the arithmetic is very simple, and
multilayered structures, non-linear boundary
conditions and variable networks can all be
handled. Programs are general in nature and are
not necessarily limited to buildings (11) .
Climatic data inputs are completely open ended
data sequences and any length of period can be
considered. Some of the well known methods of
this class, which treat the whole building and
use digital computers are discussed hereunder:
Kusuda and Achenbach(12) have used an
explicit technique to solve three dimensional
heat and mass transfer problems associated with
underground shelters. Space increments of one
foot and time increments of the order of two
hours have been taken for predicting the
temperatures for a fourteen-day period. Buchberg
et al(13) and Sheridan(14) have developed
similar types of explicit techniques for
predicting loads or temperatures in a room which
is characterised by the finite difference
representation of its elements combined in
parallel in the form of a lumped network system.
The maximum value of time increment is fixed by
stability considerations to be less than the
minimum value of the product
{C./Zd/R. .) }
which denotes the thermal time constant for the
node i connected with nodes j . The temperature
and time dependent boundary conditions
incorporating the radiative and convective modes
of heat transfer are taken into account in the
form of a delta network. Buchberg et al(13) have
also included heat exchange with the ground and
sky at the outdoor surfaces and solar radiation
penetration through windows is considered to
impinge on the floor. For calculations over long
periods of time, say a year, Buchberg and Roulet
(15) have also developed a very fast implicit type
technique and applied it to compute loads fox a
structure of homogeneous construction with no
direct solar radiation transmission and for
constant indoor air temperature. Wheway and Vahl
Davis (16) have specifically developed a method
for rooms in intermediate storeys of air
conditioned multistoreyed buildings having only
one side exposed to outside conditions and with
constant indoor air temperature. Variable shading
and reflected radiation due to adjacent buildings,
reflected radiation from ground and a variable
coefficient of heat transfer at the external
surface are taken into account. Radiation
transmission through the windows has been
considered to be a cooling load and a constant
value of the combined coefficient of heat transfer
at the indoor surfaces taken. Beckman(ll) has
developed a multimode, multinode model for systems
with combined conduction, radiation and convection
heat transfer, which can be applied to buildings.
It assumes a semi-gray enclosure and a specular-
diffuse model(17) for internal radiation exchange
and uses fifth order Hamming's method(18) to solve
the set of first order non-linear ordinary
differential equations obtained for a lumped
system. It is specifically coded to provide data
for variations in temperatures caused by changes
in the physical parameters. Non-linear boundary
conditions, variable networks and switching inputs
can be easily handled. There is difficulty in
obtaining surface temperatures as nodes with zero
capacity cannot be handled. Two major advantages
are that the time increment can be large and the
initial temperature estimates are not a critical
part of the solution.
5. Harmonic Methods
When the climatic data can be considered as
periodic cycles, which is usually the case for
design studies, the methods surveyed in this
section have a special merit on account of their
mathematical elegance and speed and ease of
computation. The input data sequences are
harmonically analysed into a steady state term and
a sufficient number of harmonics with frequencies
in integral multiples and then each one of the
pure sine waves is considered as a separate input.
The responses are then synthesised to give the
desired loads or temperatures. The main
restrictions on the applicability are that the
building system parameters have to be time
invariant, linearisation approximations have to be
used for the convective and radiative boundary
conditions and switching inputs are subject to
Gibb's phenomena (quoted in 19) as they have to be
harmonically analysed.
106
One of the earliest analyses was done by
Mackey and Wright (20) for estimating heat gains
into buildings maintained at constant Indoor air
temperature. Exact heat conduction solutions
were obtained for homogeneous elements and an
equivalent homogeneous wall (21) was defined for
multilayered constructions. Air temperature and
solar radiation impinging on an opaque element
were combined into a single input known as the
sol-air temperature (22) . Internal masses were
not considered and transmitted solar radiation
and other internal radiant loads were considered
as cooling loads directly. Degelman(23) has
computerised this method for year round usage
from first principles so as to obtain greater
flexibility in the choice of material properties,
surface coefficients of heat transfer and the
computation of solar radiation data input as
compared to the ASHRAE method(3), the earlier
version of which was based on this theory.
Nottage and Parmelee (24, 25) removed the
limitations of constant indoor air temperatures
and the internal radiant loads not being linked
to internal masses by applying the harmonic inputs
to a lumped network representation of the
building. Periodic types of inputs necessitated
the solution of only one set of simultaneous
algebraic equations for each of the harmonics as
against a very large number for numerical methods,
even though lumping errors were introduced as
before.
Van Gorcum(26) obtained an exact solution for
homogeneous slabs subjected to harmonic inputs and
showed that by analogy with passive four terminal
networks of electrical circuits, the analysis
could easily be extended to composite slabs in
series. By considering any building as a
combination of heat paths in parallel, each of
which may consist of a number of homogeneous
slabs in series, Muncey(27) devised a technique
quoted as the matrix method to predict variable
internal air temperatures, which did take into
account the internal masses. For a specified
indoor air temperature, which may be constant or
variable, this method could also be used to
predict heat gains. Pipes (28) reformulated the
method in terms of hyperbolic functions using an
electrical analogy. Gupta(29) introduced the
delta network representation of indoor radiative
convective exchanges into the method due to
Muncey(27) so as to obtain indoor air and surface
temperatures simultaneously and to allow the
transmitted radiation to be linked to internal
masses. Muncey and Spencer (30) showed that the
errors caused by taking a combined surface
coefficient of heat transfer at the indoor
surface instead of introducing a delta network
were not more than those caused by neglecting the
furniture. Depending upon the value of this
coefficient used, the calculation gave a mean
radiative-convective space temperature rather
than the air temperature. This temperature is
akin to the environmental temperature proposed by
Loudon(31). Rao (32) devised a set of thermal
system functions to calculate cooling loads by
the matrix method, which provided for temperature
swings and internal radiant loads. Gupta (33)
extended his earlier (29) scheme to take into
account multidimensional heat flow through the
ground so as to provide suitable inputs for floors
laid on ground. Muncey and Spencer (34) developed
an alternative technique to take into account
internal radiant loads without having to introduce
a delta network for indoor radiative exchange.
This extension(34) also showed how heat flow
within paths and various parallel branches in the
individual heat flow paths could be taken into
account. Gupta(35) has also interlinked the
matrix method with daylight requirements so as to
assign suitable values to Internal radiant loads
due to artificial lighting during daytime as
these acquire critical significance in determining
peak loads for open plan office buildings of large
floor areas.
The matrix type of harmonic method after
Incorporating the extensions outlined above, can
handle all types of thermal problems stated in
section 2. The requirements of system linearity
and invariability are to be observed and as such
variable networks and non-linear boundary
conditions cannot be handled. Further, the length
of the periodic design climatic cycle should be
at least twice the thermal time constant of the
enclosure(36) or more simply twice the largest
thermal time constant value amongst the heat flow
paths (37) and not merely a day if a steady
periodic regime has to be obtained inside the
enclosure.
6. Response Factor Methods
When energy requirements over a fairly long
period of time are to be assessed, the climatic
data are expected to be non-periodic and harmonic
methods are no longer applicable. Numerical
methods can still be used, but these must
introduce lumping errors. Response factor methods
have been devised so as to handle periodic, non-
periodic and intermittent Inputs equally well
without necessarily being subject to lumping
errors. The essential strategy is to determine
the system response to a unit excitation under
identical boundary conditions as for the actual
inputs. Numerical integration of the convolution
integral (10) is then carried out and the system
response is determined by superposing the unit
responses or their scalar multiples over a
significant period of time prior to the time in
question such that the actual excitations are
approximated by a succession of scalar multiples
of unit excitations. The unit response may be
characterised by a set of numbers giving the
response at equally spaced points of time or by an
influence function. These numbers or response
factors depend only on the construction and not on
the climate and can even be tabulated for
different types of constructions for handbook type
calculations. Since the principle of
superposition has to be used, the requirements of
system linearity and invariability are still to be
met. Step by step calculation, however, makes it
possible that the implications of these
requirements are not so stringent in the actual
applications as in harmonic methods. It is usual
practice to take hourly or half-hourly intervals
for load estimation but shorter Intervals may be
desirable for control systems evaluation.
107
The earliest of such techniques, due to
Nessi and Nlssole(38), calculated two influence
functions corresponding to heat flow at the
internal surface of a wall when there is a unit
step change either in the external or in the
internal air temperature. For a complete room,
the heat flows are added after being multiplied
by appropriate areas. This gives the total heat
flow at the inside surface corresponding to a
unit rise in external air temperature when the
internal air temperature is constant or else to
maintain a unit rise in internal air temperature
when the external air temperature is constant.
The former case is used to calculate cooling loads
for constant internal air temperature and the
latter by a process of inversion to determine the
rise in internal air temperature for a constant
heat flow indoors. Multilayered constructions
are approximated by a lumped system and there is
no provision for internal radiant loads.
Recently, Pratt and Ball (39) and Choudhury and
Warsi(40) have derived unit response functions by
exact analytical procedures for enclosures having
heat flow paths containing up to a maximum of
three layers.
Brisken and Reque(41) were the first to
consider response factors as a set of numbers
denoting values of a unit response function at
equally spaced intervals of time. They took the
unit excitation function as a rectangular pulse
of unit amplitude and unit time step duration and
treated the individual paths of the building as
double lump networks. Combined surface
coefficients of heat transfer were taken at the
indoor surfaces and included as part of the
networks. Heat balance methods were used at
each node to derive transfer heat admittance and
control point heat admittance parameters similar
to the influence functions of Nessi and Nissole
(40). Provision was made for internal temperature
swings but the transmitted solar radiation and
internal radiant loads were linked directly to the
indoor air. The calculations were done in two
steps namely determining the heat gains for
constant indoor air temperature and then
determining the change in indoor air temperature
for a given plant capacity or for a different
control setting. The climatic data sequences
were approximated by a succession of rectangular
pulses. The method, however, cannot handle
temperature and time dependent boundary conditions
as these form part of the lumped network
representation of the heat flow paths.
Mitalas and others have presented an improved
version of the response factor method in a series
of papers (42,43,44,45). The major points of
difference from Brisken and Reque(41) as
enumerated in (42) are that the individual layers
constituting heat flow paths are treated by exact
analysis as distributed systems, the unit
excitations are triangular pulses of unit
amplitude and twice the time step duration and
the heat transfer at the indoor surfaces of the
enclosure is represented by a delta network. The
first improvement removes lumping errors and the
computation for multilayered constructions
involves Laplace inversion of the transmission
matrix for a composite slab (43). This matrix is
the same as used for harmonic methods (26) except
for the presence of the transform parameter S.
These time series are truncated when a desired
degree of precision is obtained. Unit triangular
pulses approximate the external climatic cycles
and internal convective flows much better than
rectangular pulses as the former are equivalent to
trapezoidal approximations. However, a switching
type of input such as an artificial lighting load
could be better approximated by rectangular pulses.
The linking of Internal surfaces by a radiative
network makes the surface temperature response
factors dependent upon enclosure geometry as a
simultaneous set of heat balance equations are to
be solved. However, the surface temperatures are
calculated as part of the computations, the
internal radiant loads are distributed to the
Internal surfaces and non-symmetric elements can
be handled more easily. Also non-linear boundary
conditions (44) due to condensing or evaporative
heat transfer or due to temperature dependence of
the radiative component or due to variable wind
affecting the convective component of surface
coefficients of heat transfer can be taken into
account in this method.
The number of sets of surface temperature
re:3ponse factors is equal to the number of
excitations plus one for the room air temperature.
Cooling load response factors can be calculated
from the surface temperature response factors both
for constant air temperatures and variable air
temperatures. Once the response factors are
known, they can be combined with any set of
excitations to obtain cooling loads, air
temperatures and surface temperatures by simple
arithmetical processes. An example showing how
the time series method can be used to compute
cooling loads and to predict temperature swings
for a given capacity or for intermittent running
of the plant or to determine indoor air
temperatures is given by Stephenson and Mitalas
(45). The conditions of system linearity and
invariability still require the thermal properties
of the materials to be constant. However, variable
ventilation can be handled as the calculations of
air temperature are done step by step.
Kusuda(46) has recently extended the response
factor method due to Mitalas, Stephenson and
Arsenault to multilayer structures with various
curvatures of finite thicknesses such as spherical
and cylindrical systems and to semi- infinite
systems, such as ground. Formulae for evaluating
interfaclal temperatures and heat fluxes in
multilayer constructions have been derived and the
evaluation of response factors for multilayered
constructions has been described in detail.
Muncey(47) proposed an alternative approach
to the computation of thermal response factors of
multilayered slabs and their application to the
determination of the transient thermal response
of enclosures. Instead of finding numerically the
roots of a com-plicated transcendental equation for
the entire composite structure (43, 46) , he computed
the matrix elements for composite structures at
prespecified frequencies and used a precalculated
matrix to determine the coefficients of a large
series of exponential terms with prespecified
exponents. By selecting suitable values and a
sufficient number of the frequencies and
exponents, any desired degree of precision can be
obtained. Thus, the time consuming procedures
108
used for the Laplace inversion in the other
methods are avoided by making use of the fact that
frequency response curves in the case of
buildings are smooth and stable and point by point
matching is in order. This is because there is
no thermal analog of series capacitance or
inductance in electrical circuits.
All the previous methods use individual
response factors to obtain separate heat flows
for constant indoor air temperature and then add
them to determine cooling loads. Changes in
indoor air temperature or cooling loads permitting
temperature swings need to use another set of
response factors for the indoor air temperature
variation. Muncey et al(47,48) have developed a
procedure, which determines the response factor
for the total building pertaining to each of the
climatic sequences and internal heat loads or air
conditioning flows. This is done by determining
the indoor air temperature first and using a
combined coefficient of surface heat transfer at
the internal surfaces. However, provision exists
for linking internal masses to internal radiant
loads and accounting for heat flows occurring
internally to any path, as in the harmonic case
(37). All four types of problems mentioned in
section 2 can be handled. Both triangular and
pulse types of unit excitations are used for the
appropriate types of inputs (48). In this
method, however, it is not possible to consider
non-linear boundary conditions or variable
networks. Experience has shown that if the
calculation for sol-air temperatures takes into
account the variable outdoor coefficient of heat
transfer, using a time averaged constant value
for it in the calculation of response factors is
sufficient. Further, if the internal radiant
loads are linked to internal surfaces and not to
the air temperature, using a combined and
constant value of surface coefficient of heat
transfer at the internal surfaces is expected to
be satisfactory for building problems. Variable
ventilation can be included with certain
restrictions but only at the cost of analytical
rigour,
7. Conclusions
A wide variety of computer oriented thermal
calculation methods pertaining to buildings have
been considered in relation to the concepts they
use, the assumptions they employ and the
limitations in regard to their applicability. No
attempt has been made to compare their validity
with respect to actual buildings or their
efficiency in terms of computer time. This can
only be done by using all of them for the same
large size actual building and comparing the
estimates with the experimentally observed data
and the actual computation costs incurred,
i.e. by instituting some sort of round robin
test. In a fast developing discipline, like the
subject of this survey it is very likely that
some conceptually significant methods may have
escaped the notice of the authors and the
omissions, if any, are not intended to reflect on
the methods.
8. References
(1) Milbank, N.O. and Harrington-Lynn, J.,
Estimation of Air conditioning Loads in
Air Conditioning System Design in Buildings,
p. 41 (Elsevier, ).
(2) Gupta, C.L., Heat transfer in buildings - a
review. Arch. Scl. Rev. 21,1 ().
(3) ASHRAE Handbook of Fundamentals, New York,
().
(4) Carrier Handbook of Air conditioning
System Design (McGraw Hill, ).
(5) Boeke, A.W. , New developments in the
computer design of air conditioning systems,
J.I.H.V.E, 35,195 ().
(6) Korsgaard, V. and Lund, H. , Air conditioning
load calculations by means of a passive
electrical analogue computer. World Power
Conference, IV-B, Paper 63 ().
(7) Button, D.A. and Owens, P.G.T.,
Considerations for the optimized fabric
design. Engineering in the home, p. 64
(Allen & Heath, ).
(8) Euser, P. , De Toepassing Van Analogons Blj
Het Oplossen Van Warmteoverdrachts-problem,
De Ingenieur J_7, ().
(9) Stephenson, D.G. , Methods of determining
non steady state heat flow through walls
and roofs of buildings, J.I.H.V.E. 30,64
(),
(10) Carslaw, H.S, and Jaeger, J,C, , Conduction
of Heat in Solids (Oxford University Press,
).
(11) Beckman, W,A, , Solution of heat transfer
problems on a digital computer.
International Solar Energy Society
Conference, 7/66 (),
(12) Kusuda, T, and Achenbach, P,R. , Numerical
analysis of the thermal environment of
occupied underground spaces with finite
cover using a digital computer. Trans.
ASHRAE 69,439 ().
(13) Buchberg, H, , Bussell, B. and Reisman, A. ,
On the determination of optimum thermal
enclosures, Int. J.Brodim.Bromet _8,103
().
(14) Sheridan, N.R. , Energy conservation applied
to the rational design of a dwelling for
the tropics, World Power Conference, IV-B,
Paper 54 ().
(15) Buchberg, H. and Roulet, J.R. , Simulation
and optimization of solar collection and
storage for house heating. Solar Energy
22,31 ().
109
(16) Wheway, R.T. and Vahl Davis, G.De. ,
Calculation of transient heat flow into
buildings, ASHRAE Jl.8,67 ().
(17) Bobco, R.P., Radiation heat transfer in
semi-gray enclosures with specularly and
diffusely reflecting surfaces. Trans. ASME,
Ser.C. 86,123 ().
(18) Hamming, R.W. , Numerical methods for
scientists and engineers, (McGraw Hill,
).
(19) Guillemin, E.A. , Mathematics of circuit
analysis, (John Wiley, ).
(20) Mackey, CO. and Wright, L.T. , Periodic
heat flow - homogeneous walls and roof,
Trans. ASHVE 50,293 (194A).
(21) Mackey, CO. and Wright, L.T., Periodic
heat flow - composite walls and roof.
Trans. ASHVE 5^,283 ().
(22) Mackey, CO. and Wright, L.T. , The sol-air
thermometer, a new instrument. Trans.
ASHVE _52,271 ().
(23) Degelman, L.O., The development of a
mathematical model for predicting solar
heat gains through building walls and
roofs. Better building report No. 6,
(Penn. State University, ).
(24) Nottage, H.B. and Parmelee, G.V., Circuit
analysis applied to load estimating Pt.I,
Trans. ASHAE 60,59 ().
(25) Nottage, H.B. and Parmelee, G.V. , Circuit
analysis applied to load estimating Pt.II
Trans. ASHAE _61,125 ().
(26) Van Gorcum, A. , Theoretical considerations
in the conduction of fluctuating heat flow,
App.Sci.Res A2,272 ().
(27) Muncey, R.W. , The calculation of
temperature inside buildings having
variable external conditions, Aust.J.Appl.
Sci 4_,189 ().
(28) Pipes, L.A. , Matrix analysis of heat
transfer problems, J.Franklin Inst. 263, 195
().
(29) Gupta, CL. , A matrix method for predicting
thermal response of unconditioned buildings,
J.I.H.V.E. ^,159 ().
(30) Muncey, R.W. and Spencer, J.W. , Calculation
of non-steady heat flow : considerations of
radiation within the room, J.I.H.V.E.
34,35 ().
(31) Loudon, A.G., Summertime temperatures in
buildings without air conditioning, BRS
cp 46/68.
(32) Rao, K.R. , Accurate estimation of air-
conditioning load of buildings, Proc. Third
Aust.Bldg Res.Congr., Melbourne, ,
162 ().
(33) Gupta, CL. , Some heat transfer problems
with application to buildings. Chap. 8. Ph.D.
Thesis, University of Roorkee, .
(34) Muncey, R.W. and Spencer, J.W. , Calculation
of temperatures in buildings by the matrix
method : some particular cases, Bldg.Sci.
3,227 ().
(35) Gupta, CL. , A systems model for
environmental design of buildings (in this
symposium) .
(36) Raychaudhuri , B.C., Transient thermal
response of enclosures : the integrated
thermal time constant. Int. J. Heat Mass
Transfer 8, ().
(37) Billington, N.S., Building Physics - Heat,
p. 68 (Pergamon, ).
(38) Nessi, A. and Nissole, L. , Fonctions
d' influence de flux de Chaleur des parois
de construction. Rapport . Comite Tech.
Indus. Chauffages (Paris, ).
(39) Pratt, A.W. and Ball, E.F., Transient
cooling of a heated enclosure. Int. J. Heat
Mass Transfer 6^,703 ().
(40) Choudhury, N.K.D. and Warsl, Z.U.A. ,
Weighting function and transient thermal
response of buildings. Int. J. Heat Mass
Transfer 2, ().
(41) Brisken, W.R. and Reque, S.G., Heat load
calculations by thermal response. Trans.
ASHVE 62,391 ().
(42) Mitalas, CP. and Stephenson, D.C, Room
thermal response factors. Trans. ASHRAE,
Paper ().
(43) Mitalas, CP. and Arsenault, J.C, Fortran
IV program to calculate heat flux response
^ factors for multilayer slabs, DBR computer
program no. 23 (NRC Canada, ).
(44) Mitalas, CP., Calculation of transient heat
flow through walls and roofs. Trans. ASHRAE
74,181 ().
(45) Stephenson, D.C and Mitalas, CP., Cooling
load calculations by thermal response
factors. Trans. ASHVE 23, Paper no. ,
().
(46) Kusuda, T. , Thermal response factors for
multi-layer structures of various heat
conduction systems. Trans. ASHRAE 75,246
().
(47) Muncey, R.W. , The thermal response of a
building to sudden changes of temperature
or heat flow, Aust.J.Appl. Sci. 14, 123
().
(48) Muncey, R.W. , Spencer, J.W. and Gupta, CL. ,
Method for thermal calculations using total
building response factors (in this
symposium) .
110
Method for Thermal Calculations using Total Building Response Factors
by R. W. R. Muncey*, J. W. Spencer"*" and C. L. Gupta"*"
Thermal calculations for buildings may be conveniently undertaken by
multiplication of the time sequence of climate parameters and the response factor
of the building for each parameter. The true response factor is the sum of an
infinite number of exponential terms which may be approximated by truncation
directly or by matching the response with a chosen number of exponential terms
having prespecified time constants.
Computationally the latter method is attractive because it may use the
response values for the building to sinusoidal changes of a number of prespecified
frequencies. The combination of the behaviour of the various heat paths is then
relatively simple irrespective of the number of layers in any one path and even if
branches or heat flows occur within some of the paths.
The process involves calculation of the thermal response of the separate heat
paths relevant to the climate parameters at the steady state and at a set of 18
frequencies, the combination of these responses to determine the total building
response to any one climate excitation and multiplication by a precalculated matrix
to give the exponential series for the response factor. It has been found that
the errors introduced in the matching process are insignificant when compared with
the inaccuracy in knowledge of the building's thermal properties and of climatic
data.
Because, in the normal heavy building, the response factor even at 10 days is
not completely negligible, some method is desirable to reduce the data bank
necessary to store the total building response factor. This is achieved by
calculating and retaining the values at hourly intervals to 6 hr and at times in
the ratio of l:/2 upwards from 0.177 days (and including h, h, 1» 2, A ....days).
Results will be shown as obtained by use of a Control Data computer and
an indication given of approximate means for overcoming the inherent shortcomings
of this and comparable methods.
Key words: Building, computer, exponential series, harmonic, indoor
temperatures, matrix, response factors, step function, thermal.
1. Introduction
The growing desire to understand the internal
thermal environment of buildings and the greater
need to tailor the capacity of air conditioning
devices have led to notable improvements in the
calculation methods available. With the advent of
electronic digital computers giving improved
speed, complexity and reliability in comparison
with earlier methods, it is no longer necessairy to
restrict investigation to simple cases or to adopt
simplifying assumptions of doubtful validity.
The data commonly available for use in
specific cases consist of a knowledge of the
structure and its orientation, the dimensions and
thermal properties of its components and the
climatic variables expressed as time sequences,
generally at hourly intervals, of the parameter
values. These inevitably relate to past cycles
and the calculation may use a set derived from an
earlier specific occasion or a set representative
of earlier occurrences averaged by a selected
method not relevant at the moment. Sequences for
external air temperature, sol-air temperatures of
various surfaces, sunshine penetration of windows
and internal heat loads are the most suitable and
will be used hereunder although other series
defining comparable climatic variables could be
used.
*Division of Forest Products, CSIRO, Melbourne, Australia
"'Division of Building Research, CSIRO, Melbourne, Australia
111
Several assumptions are implicit in even the
most sophisticated methods presently of interest.
It is almost universally assumed that the
transmission through the various paths
(e.g. walls, floor, roof) is unidimensional and
that the effects of corners and lumped
construction such as wall studs and roof rafters
may be ignored. Constancy of thermal values of
conductivity and heat capacity is assumed even
although these are known to vary somewhat with
temperature and moisture content. Film
resistances are commonly also assumed constant
and current work by the authors suggests this
assumption does not introduce errors of an
unacceptable magnitude. Muncey and Spencer^ ^
showed that the transfer of heat between the
bounding surfaces of a room could be treated
adequately by a star network connecting each
surface to a "mean convective- radiative
temperature" for the errors thereby introduced
are less than those caused by neglecting the
presence or the location of furniture.
2. Overall Strategy
A fonvenient method, when one has available
sequences describing climatic data, is to
determine response factors which connect the
temperature or heat flow to be calculated with
the climatic data by a relation
internal temperature = 2 (response factor x
climatic data sequence)
(1)
/ 9 l
A well known method (Nessi and Nissole^ -'j
Brisken and Reque' , Stephenson and Mitalas^^-^
Kusuda^^O determines the response factor relating
the heat flow (with a constant internal
temperature) for each path separately and thence
evaluates the total heat flow. By finding the
response of the internal temperature to a step
function or unit pulse heat flow to the inside,
it is readily possible by an Inversion process to
evaluate the internal temperature conditions
within or following a given climatic data
sequence.
This paper will describe a method which
evaluates the response factor for the total
building, there being a particular set of response
factors corresponding to each external climatic
sequence and to internal heat loads or air
conditioning heat flows. The response factor for
a total building derives from the sum of several
sets of an infinite series of exponential terms,
the number of sets being n I if there be a total
of n "slabs" within the several paths for heat
flow within the structure. As the value of n
might easily reach 20, and since the exponential
decrements are related to the solutions of
transcendental equations with values dependent on
the thermal properties of the structure, the
complexity of the exact solution needs no
emphas is .
One method that might be used in a search
for simplicity is to truncate the series
described and it is common to find that, except
for very short intervals (i.e. soon after the
initiating pulse) appropriate accuracy can be
achieved with only one or two terms. An
alternate method is used here. In this the
response is calculated for the steady state and
for cases where the external driving stimulus is
sinusoidal. The building can readily be treated
as a whole (i.e. the effect of the several paths
may be combined) even if parallel paths occur as
arms within a particular identified path or heat
flows occur at points internal to the path
(Muncey and Spencer^S)). By suitable choice of
the frequency of the stimulus and by using an
adequate number of frequencies, the response may
be characterised with any desired degree of
precision. It will then be shown that, from
these sinusoidal responses, by multiplication by
a precalculated matrix, the coefficients of a
large series of exponential terms with
prespecified time constants can be evaluated.
Again, any desired degree of precision can be
achieved by using sufficient exponential terms.
In the work being described, 18 terms are used
with the (angular) frequency of the sinusoidal
variations ranging from 1 in 768 hr to 170 2/3
per hr and the time constants ranging from
768 hr to 3/512 hr. The total errors
introduced by the use of only 18 terms are of
the order of 0.01 per cent, for cases where the
time constants are of the order of 1 hr to
1 day.
3. Harmonic Response
An individual homogeneous slab of infinite
area with sinusoidal temperatures on and heat
flows across the faces can be considered using
the same mathematics as for an electrical
"four pole" (Van Gorcumt7}, VodickafSl), The
surface temperatures T^^ exp(jojt) and T^ exp(ju)t)
and the heat flows Wj^ exp(j(jot) and W2 exp(jiot)
are related as follows:
cos H -(R sin H)/H
Tl
W2
(H sin H)/R cos H
wherein R is the thermal resistance of the slab
per unit area, c is the thermal capacity of the
slab per unit area and H = (jaiCR)'^.
*Figures in brackets indicate the literature references at the end of this paper.
112
Van Gorcum further showed that, if slabs were
placed in series with intimate contact over their
surfaces, the matrix connecting the temperatures
and heat flows over more than one slab could be
found by multiplication of the individual
matrices.
An individual heat path in a building can be
represented by a number of slabs in series and
the total building with its several heat paths by
several of these groups in parallel. If the
matrix for a typical heat path of area A
connected to an external climatic element be
^11
^12
p =
^21
^22
and that of a typical
neat
path
connected to a face over which no heat flows
(e.g. half a symmetrical wall exposed on each side
to the same temperature) be
Qll ^12
^21 ^^22
and if the value of the sinusoidal temperature be
exp(ju)t) externally and T exp (jiut) internally
and the heat flow to the inside (air) be W exp(ju)t)
then
IAT^(1/P^2) - W
IA(P^^/P^2) + 2:b(Q2i/Q22)
shown by Muncey^9,10} and Pipes'- ,
(3)
Step Function Response
Consider a thermal circuit as shown in
figure 1 with a driving stimulus at D and a
response at R. The stimulus may be an imposed
temperature or a heat flow and connecting
circuits may have any configuration (series,
parallel or series-parallel) and some may not be
present in the specific case. The steady state
response x^ at R due to a unit stimulus at D and
the periodic response Xq + + iV-^) exp(ja)j^t)
at R due to a stimulus exp(j(i^t) at D can be
found for relevant by the method outlined in
the previous section. It is desired to find the
response g + f g exp(-b t) at R corresponding
0 n=I n n
to a unit step function at D. Consideration of
the response at large values of t will show that
The periodic stimulus exp(ja)^t) may be
considered as the result of innumerable
infinitesimal step- function stimuli ju^^exp (ju^^t) 6t
occurring from infinite time past.
Applying the step-function response to each
stimulus and adding, the harmonic response is
ja)j^exp(ju)^t') [Bq + I^^ B^exp(-b^(t-t'))] dt'
3<\
i.e. BQexp(ja)^t) + B^
exp (jiJ), t)
Equating the response from the two methods and
ons remain
Each equation
removing B^ and x^, a series of equations remain
for evaluation of the values of B
has the form ^
n=l
0, + ib 0),
k n k
+ to,
~ \ = \ j^k
and the whole may be represented in matrix form
|R|.|B|=|x| and |s|.|B|=|y|
Presuming that the nxjmber of n's and k's are the
same, the values of the B's may be found from
either set of equations as
iBl = IR
■1
B
The same problem is handled by an alternate
{ 1 ?}
method by Muncey .
5.
Practical Evaluation
The method outlined would be merely
theoretically interesting if a number of conditions
are not fulfilled. It is desirable that, to
achieve an acceptably accurate result in
representing the thermal change;
(a) the number of harmonics and exponential
terms is not excessive
(b) the range of frequencies and time constants
adequately covers the area of interest
(c) the elements in the inverted matrix | R|
or I S are not excessive
(d) the exponential coefficients are not large
compared with the thermal change.
An early choice, which has been found to
satisfy these conditions very satisfactorily, is
as follows:
113
(a) the values of bj and ui-^, i.e. the inverse
time constant of the exponential and the
angular frequency, to be equal
(b) the ratio between successive b's and u's
to be 2:1
(c) the total number of harmonics (and
exponential terms) to be between 10 and 20.
In the presently used calculation the
number is cfiosen as 18. This choice gives an
angular frequency from 1/768 hr to 170 2/3 per hr
and time constants from 768 hr (32 days) to
3/512 hr (21 sec) which adequately covers the
range of interest. The |s| matrix is symmetrical
and |s|~^ matrix has values up to 30.07. The
quarter matrix is given in Table 1. It should be
noted that by calculating the matrix inverse for
increasing sizes, it can easily be seen that each
row in the infinite matrix would have the values
given in Table 2 in order from the diagonal to
the left and right and thereafter the ratio from
one element to the next is -0.5. In a matrix of
large order the elements close to the top left
and bottom right corners (within say 6 rows or
columns) are very close to those given in
Table 1. All this implies that the coefficient b
is largely fixed by the values y of the harmonic
response at frequencies to close to b, a result
that is not really surprising. . ,
The above treatment relates to the response
to a step function excitation. It is more
suitable, in representing the external climate, to
assume a linear change to occur between successive
values of the climatic data. This can be achieved
by transforming the step function response to give
the response to one of the excitation patterns of
figure 2 for temperature or heat flow.
It can readily be shown by Integrating the
response at time t from t-1 to t (fig. 2 (a)), by
differencing the responses at times t and t-1,
each being integrated from t-1 to t (fig. 2(b)), or
by differencing the responses at times t and t-1
(fig. 2(c)) that the factors by which the term
exp(-b^t) must be multiplied are
t = 1
Figure 2(a) (exp(b )-l)/b
n n
t > 1
(exp(b^)-l)/b^
Figure 2(b) (exp (b^)-l) /b^ -(exp(b^)-l) /b^
Figure 2(c)
1 - exp(b^)
Table 1. One Quarter of the Symmetrical 18 x 18 Inverse Matrix
, 7.
-10.
21.
6.
-19.
27.
-3.
11.
-22.
29.
1.
,
-6.
13.
-23.
29.
-0.
,
3,
-7,
13,
-23.
30.
,
0.
,
-1.
3.
-7.
14.
-24.
,
30.
-0.
,
0.
-1.
3,
-7.
14.
,
-24.
30,
0.
,
-0.
0.
-1.
3.
-7.
.
14.
-24.
-0.
.
0.
-0.
0.
-1.
3.
.
-7.
14.
0.
,
-0.
0.
-0.
0.
-1.
,
3.
-7.
-0.
0.
-0.
0.
-0.
0.
,
-1.
0.
,
-0.
0.
-0.
0.
-0.
,
-0.
,
0.
-0.
0.
-0.
0.
,
-0.
0.
-0.
-0,
.
0.
-0.
0.
.
-0.
-0.
.
30.
-24.
Table 2. Major Elements in the Infinite Inverse Matrix
30. -24. 14. -7. 3. -1. 0. -0. 0.
114
It should be noted that these factors can
range in magnitude from 10"^ to lO^^^ and that
the steady state term Bq remains at all times
when using the pulse shape of figure 2(a), but
cancels at times later than t = 1 for the pulse
shapes of figures 2(b) and 2(c). The authors
have found it most convenient to use the pulse
type of figure 2(a) for temperature changes, that
of figure 2(b) for solar heating through windows
and that of figure 2(c) for "air-conditioning"
and internal heat flows.
With exponential time constants ranging up
to 32 days it is obvious that the steady state
may not be approximated satisfactorily even at
50 days. Storage of behaviour at hourly intervals
would require memory cells for each heat
path in each building and a similar storage for
either each temperature sequence or future
temperature accumulation. This huge store demand
has been reduced by the following device. The
response factor for each path of the building and
the accumulation of future temperatures is
undertaken for 1, 2, 3, 4, 5 and 6 hr and for
3 X 2^ 3 X 2^'\ 3 X 2"\ 3 x 2^'^
18/2
3x2 hr and the future accumulator for
3 X 1^^'^ and 3 x 2^°''^ hr (90.5 and 128 days) set
18/2
equal to that at 3 x 2 hr (64 days).
Acciunulation at each future time is made by
adding the product of the climate parameter for
each path by the response factor for the relevant
path and time.
Following suitable "thermostat" procedures,
the time marker is moved one hour and the new
accumulator values are found as follows :
by substitution from
previous 2 to 6 hr values
by interpolation as
described later
1 to 5 hr
2/2
3x2' hr to
64 days
64/2 and 128 days by copying the 64 day value
2/2
6 hr by copying from 3x2 hr
\,
3 X 2 ^ hr by second order Bessel
interpolation using linear
time and the values for
3, 4, 5 and 6 hr.
In the series from 6 hr to 64 days the value
for (3 X 2"'/2 + 1) Q^d time (i.e. 3 x 2™/2 hr
new time) is found by second order Bessel
interpolation with a logarithmic time scale.
Calculations for cases recognized to be difficult
to match with the chosen exponential series and
operation of the repeated interpolation process
have been shown to introduce errors of the order
of 0.01 per cent, in conditions normally of
interest in buildings.
Implementation
Computer programs to enable such
calculations to be undertaken have been written
for an Elliott 803 computer and more recently a
Control Data computer. Since only time
units are implicit in the program, it is capable
of operation in any consistent system of units.
Refinements allowing detailed data checking,
calculation of solar position, sol-air
temperatures and heat flows consequent on
radiation transmitted by windows have been
included. Very lengthy climatic sequences can
be handled and the total memory required for the
program is of the order of 28K cells. Allowing
for heat path groups and 12 heat paths plus
thermostat ventilation, heating and cooling paths,
10 buildings can be accommodated at one time.
The whole calculation for one building with say
10 heat paths and a 21 day sequence considered
hourly requires about 40 seconds computational
time.
7.
{1} Muncey, R. W. and Spencer, J. W. ,
Calculation of non-steady heat flow;
considerations of radiation within the
room, J.I.H.V.E. 34 35-38 ().
{2} Nessi, A. and Nissole, L. , Fonctions
d' influence de flux de chaleur des parois
de construction, Rapp.Com.Tech.de I'Ind.
du Chauff. et la Vent Paris, ().
{3} Brisken, W. R. and Reque, S. G. , Heat load
calculations by thermal response, ASHRAE
Trans. 62 391-419, ().
{4} Stephenson, D.G. andMitalas, G. P.,
Cooling load calculations by thermal
response factor method, ASHRAE Trans. _73^
III. 1.1-7 ().
References
{5} Kusuda, T. , Thermal response factors for
multi-layer structures of various heat
conduction systems, ASHRAE Trans. 75
246-270 ().
{6} Muncey, R. W. and Spencer, J. W. ,
Calculation of temperatures in buildings
by the matrix method : some particular cases.
Build. Sci. 3 227-229, ().
{7} van Gorcum, A. H. , Theoretical considerations
on the conduction of fluctuating heat flow,
Appl. Sci. Res. Hague A2 272-80 ().
{8} Vodicka, V., Conduc tion of fluctuating
heat flow in a wall consisting of many
layers, Appl. Sci. Res. Hague A5 108-14
().
115
{9} Muncey, R. W. , The calculation of
temperatures inside buildings having
variable external conditions,
Aust.J.Appl.Sci. _4 189-96 ()
{10} Muncey, R. W. , Calculation of heat flows
and temperatures in slabs in series,
parallel and series-parallel,
Appl.Sci.Res. Hague A5 461-62 ().
{11} Pipes, L. A., Matrix analysis of heat
transfer problems, J. Franklin Inst.
263 195-206 ().
{12} Muncey, R. W. , The thermal response of
a building to sudden changes of
temperature or heat flow, Aust.J.Appl.Sci.
14 123-128 ().
!
•
D
R
Figure 1. Generalised thermal circuit,
driving stimulus at D, response at R.
Figure 2. Temperature or heat flow excitation pulse shapes.
116
Calculation of Building Thermal Response Factors (BTLRF) as Wiener Filter Coefficients
T. Kusuda
National Bureau of Standards
Washington, D, C.
Recent advances in the application of computers for environmental engineering
problems have brought forth a number of sophisticated computer programs for simu-
lating the hour by hour thermal performance of buildings. These programs not only
calculate hourly thermal load of the building spaces, but also simulate the opera-
tion of energy distribution systems and mechanical equipment. When applied to a
large building, however, the amount of computations to be performed become formi-
dable even for the modern high speed and large memory computers. One way to reduce
the computational requirement and to save the computer time (and cost) is to use
building thermal response factors, (BTLRF), which are secondary sets of numbers
derived from the limited amount of detailed calculations which are obtained from
the exact thermal analysis. Presented in this paper is a preliminary attempt to
apply time series analysis for obtaining BTLRF of a single room building. It is
pointed out that BTLRF could also be obtained from measured thermal performance
data or energy consumption data.
Key Words: Building thermal load response factors, energy requirements,
heating and cooling load calculation, Wiener filters
1. Background
Calculations to determine the heating and cooling load for use in predicting building energy re-
quirements can now be done by many digital computer programs. Although differing in minor technical
details, most of the current computer programs for energy calculation obtain the hourly thermal load
in conjunction with hourly weather tape data as provided, for example, by the National Weather Record
Center.
This hour by hour calculation of energy requirements, based upon detailed simulation of building
thermal response, has been considered more accurate for a wider type of buildings than other simplified
techniques, commonly known as the "degree day method", the "equivalent load factor method" and the "bin
method"i!l/. These simplified methods are based upon the assumption that the building thermal performance
can be calculated by a simple linear function of outdoor air temperature, particularly the temperature
difference between the out- and indoor air. The temperature difference concept of the simplified tech-
niques ignores the fact that the building thermal load is also dependent upon the other factors, such
as solar radiation, moisture content of air, internal heat generation, and heat storage of the building
structure. The simplified methods based upon the linear temperature difference concept have been, how-
ever, considered relatively accurate for use in residential applications, mainly due to the fact that
the effect of solar radiation is relatively small and the internal heat generation is small and rela-
tively constant as compared with commercial or industrial buildings.
Senior Mechanical Engineer, Environmental Engineering Section, Building Research Division
Although numerous references are available for these traditional methods, the most convenient one
will be the ASHRAE Guide and Data Book, Systems , Chapter 40, pp. 619-634.
117
The factors that have justified the use of the simple temperature difference concept become increas-
ingly inappropriate as the building becomes larger and operational and occupancy characteristics grow
complex. For example, the solar radiation effect becomes extremely important when an exterior wall of
a modern office building is largely glass. For another case, internal heat generation due to the heavy
lighting power per square foot of floor area tends to eclipse the indoor-outdoor temperature difference
effect on the thermal load. Added to the complexity of these characteristics of the modern large scale
building is the sophisticated nature of the heating and cooling system and its controls, for distributing
excess internal heat of the building core to the periphery to limit the heating requirements during the
winter.
The hourly load simulation method with the use of computers performs an algorithmic operation which
is designed to follow the actual thermal performance of buildings under realistic or randomly fluctuating
outdoor weather conditions. One of the difficulties involved in using the sophisticated and exact hourly
calculation of building thermal performance is that a large amount of computer and memory time is needed.
For example!./, the computer program developed by the U. S. Post Office Department requires a 100 K core
storage computer (if applied to large postal facilities) and approximately 2 minutes of UNIVAC time
to obtain an energy requirement estimate for heating and cooling of one room for a period of 365 days.
If the calculation is to be performed for a large building consisting of, say 100 different rooms, the
total computation time becomes prohibitive. This is particularly so when the building characteristics
under consideration are complex, and when the accuracy requirement is such that the simplification of
the computational efforts may be risky. The reduction of the computational effort is usually accomplished
in two different ways. The first is to simplify the algorithms such as to delete refined calculation
routines (thermal storage effect and infiltration effect). The second method is to simplify the build-
ing structure such as to treat a multi-room building as a single room building by ignoring the heat ex-
change among rooms and by ignoring details of the building structure. However, it has not been well-
established xinder what conditions these computational shortcuts are justified. But in addition to
these two, also presented in this paper is a preliminary attempt to study a third alternative for the
reducing computational requirement, with a reasonable accuracy. Its objective is to obtain a secondary
set of numbers called the building thermal load response factors (BTLRF) from the results of a limited
number of detailed calculations.
2. Building Thermal Response Factors (BTLRF)
These building response factors are basically regression coefficients as it becomes clear in the
later discussion. The primary assumption imposed upon this technique is that the building thermal
loads are a linear function of various excitation parameters such as outdoor temperature, solar radia-
tion, internal heat generation and as well as the indoor temperature^'.
It is also assumed that the stochastic characteristics of the thermal load as well as the excita-
tion time parameters are stationary, meaning that their basic means and standard deviation do not change
with respect time.
As a matter of fact, it is important to point out that the basic technique used to derive these
building response factors can be applicable to any time series relationship, whether it be the heating/
cooling load, energy requirement, space thermal load or building thermal load. The time series, there-
fore, could be the observed energy usage values rather than the calculated values as mentioned previ-
ously. The idea is to derive regression coefficients from any input and the output time series by a
suitable regression technique.
For example, the hourly room thermal load may be calculated by a detailed computer program for a
predetermined period (say N hours). The calculated hourly thermal load is then the desired output time
series whereas the dry-bulb temperature, solar radiation and the internal heat generation may be con-
sidered input time series or the excitation time series.
Denoting the hourly values of the thermal load, outdoor dry-bulb temperature, room temperature,
solar radiation and the internal heat generation by q, DB, T, SOL and LT, respectively, it is assumed
that the following linear relationship exists among them.
M / DB - T
t-s t-s
L
t-s
''t ~I (fi(s), £^(3), f3(s)) I SOL 1 , t - 1, 2 ... N (I)
LT^
t-s
- The constant factor relating the degree days data to the energy requirement is a simplified
BTLRF when the temperature difference is the major contributor to the energy requirement.
118
In this expression fj^(s), £2(3) and f^Cs) for s = 0, 1, 2 ... M are the regression coefficients for the
excitation parameters, temperature, solar radiation and the internal heat generation respectively. Sub-
script t in eq. (1) refers to the hour at which q is calculated and t-s refers to DB, T, SOL and LT
evaluated at t-s hour.
These regression coefficients are called the Wiener filters [1] if they are determined in such a
way that
N
6=Y(q^-q;)' (2)
t=l
in minimum, whereby the q' is the value obtained by the exact calculations taking into account the
building details and, or the desired output time series, whereas q^ is the value approximated by eq.
(1) solely on the basis of time series analysis of participating variables.
In eq. (2) N is the total number of data points to be analyzed to arrive at the least squares re-
gression coefficients or Wiener filters. For example, if the two weeks data were used for the hourly
thermal load calculations, N should be 336.
A computer program to obtain the Wiener filters coefficients has been developed and published by
E. A. Robinson [2]. The progrcun utilizes a recursion type solution of multi-channel normal equations
of the data to be processed. Given in the following section are examples of the application of the
Robinson's computer program to the heating and cooling load calculation by the thermal analysis pro-
gram [2] of the U. S. Post Office Department (USPOD).
3. Sample Calculations
In order to examine the feasibility of the use of the Wiener filter routine to obtain BTLRF as the
least square regression coefficients, hourly heating and cooling loads of a one-room building was first
computed for 336 hours by the USPOD program. The weather data used for the calculation were for Janu-
ary of Washington, D. C.
Figure 1 shows the trend of the excitation functions, namely the dry-bulb temperature, solar radi-
ation and internal heat generation during the computation periods.
In order to simplify the calculation, the room temperature, T^ , in eq. (1) was assumed constant at
75 °F. When the calculated thermal load was plotted against the outdoor temperature and against the
solar radiation, they showed very much scatter as shown in figures 2 and 3 respectively. Figure 2,
for example, suggests a danger of estimating hourly thermal load by a linear relationship with outdoor
air temperature alone.
The Wiener filtering technique was applied to the calculated thermal load regressed with
(DB-75) , SOL and LT^ for eq. (1) for s = 0, 1, 2, . . . M.
t-s t-s t-s 1 K J
The value M in equation (1) is called the filter length and is related to the delayed reaction of
the thermal load q^. with respect to the excitation parameters. A satisfactory value for M may be deter-
mined by letting M = o, 1, 2 ... in eq. (1) until further increase does not significantly decrease the
value of 6. In this particular example, values of M up to 20 have been tried and it was found that the
optimum value is 3 for all the practical purposes.
In order to illustrate building response factors for M = 3, the filter coefficients for a one-room
building are listed as follows:
f^iO) = 31.913 f2(0) = 3.807 f^CO) = 4.308
fj^(l) = -.426 f2(l) = -.056 f^d) = 1.809
fj^(2) = -.267 f2 (2 ) = 1.777 f 3 (2 ) = 1.762
fj^O) = -.245 f2(3)= 1.110 £3(3) = 2.639
119
Normalized values— of 6 for M = 0, 1, 2 ... 10 respectively for a similar analysis are 0.219, .137,
.093, .067, .062, .057, .054, ,053, .050, and .047, which show the diminishing return for M beyond 3.
It should be pointed out that it is difficult to draw physically meaningful conclusions from these
coefficients, since they were derived solely by numerical data manipulation. Nevertheless, they simu-
late thermal load very accurately for the period where the original data were analyzed. Also to be
pointed out is the reduction of mathematical operation manifested in a simple algebraic formula of
equation (1) against a detailed thermal analysis program consisting of approximately Fortran
statements.
It is, however, to be expected from the theory of heat conduction equation that the absolute
values of BTLRF should start to decrease steadily—' as the value of s increases beyond a certain value,
say S , such that
max
.... fj^ (S+3)
when S > S
max
This decreasing trend was not observed for this sample calculation even when M was carried up to 20,
although it is possible that filter coefficients of more physically consistent nature might have been
obtained, had a suitable smoothing technique been applied to the input data.
Although these response factors did reproduce the original data very well, a true test of the res-
ponse factors would be when they are applied in a predictive manner. Figure 4 shows the same response
factors applied to eq. (1) for the climatic data beyond the period when the original thermal load was
calculated. Figure 5 is in turn the thermal load calculated by the USPOD program for the same weather
record period. If the response factors are ideal, figures 4 and 5 should match each other well for the
entire period.
By overlaying figure 4 on figure 5 it can be shown that the two curves match almost perfectly for
the first 336 hours during which period the response factors were generated. The same two curves, how-
ever, begin to differ considerably as the time goes beyond the first 336 hours and particularly during
the summer period, although general trend of the increase of the mean thermal load is obtained by the
response factor calculation. The increase of the diurnal amplitude of the thermal load during the
summer, however, was not well represented by the calculation using BTLRF.
The similar calculation repeated for 336 hours (two weeks period) data of thermal load and accom-
panying weather data during the last week of June yielded another set of building response factors
such as :
fj^(O) = 39.497
h
(0) =
11.558
f3(0) =
7.2 06
f^(l) = 15.488
h
(1) =
-4.362
f3(l) =
1.668
f^(2) = -50.894
h
(2) =
-4.177
f3(2) =
1.789
f^(3) = 38.594
(3) =
10.768
f3(3) =
1.650
These values were in turn used again to calculate the hourly building thermal load from January to
June by eq. (1), results of which are shown in figure 6.
The agreement between the thermal loads obtained by the detailed calculation with use of USPOD
program and those approximated by eq. (1) is poor during the winter this time. The decrease of the
average values and amplitudes of the building thermal load during the winter is not well reproduced.
These dwo sets of calculations and figures 4 and 6 suggest that the BTLRF can be made a function
of time.
It is assumed that they will change from set (3) to (4) by a linear fashion such that:
[f(t)] = [fj + [fj (1 - 5^) (5)
where [f ] and [f ] represent the winter and summer building response factors and [f] is those adjusted
with tune.
f^ (S+2)
f^ (S+1)
(S)
120
The value of §^ in eq . (5) was assumed to be a step time function representing:
P = Integer part of (t/336) . .
5t 12
for the 12 bi-weekly periods spanning the beginning of January through the near end of June.
The result of this calculation is shown in figure 7, and indicates a better agreement with the
detailed calculations (figure 3) obtained by the USPOD program throughout the period than figures
4 and 6. The agreement should be further improved if the values of BTLRF were made a more complex
function of time than a simple linear function.
4. Summary
A possible new approach to enhance the use of computers for calculating building thermal load is
the application of Wiener-type filter coefficients which are called in this paper the BTLRF or the
building thermal load response factors. It is pointed out in this paper that BTLRF can be obtained
either from the heating/cooling load calculated by the very comprehensive computer program (simulating
entire building heat transfer processes) or from the experimentally observed values for a limited
period of time, say two weeks. Once determined, these BTLRF can permit the calculation of the thermal
load by one simple linear algebraic equation. This results in drastic reduction of the computational
effort as well as the core requirement on the computers, from a computer program needing a few thousand
Fortran statements and 100 K core storage computer to a program of a few Fortran statements that can be
executed on a mini- computer . A rough estimate of computer time reduction is from 2 minutes per room of
a building to a few seconds per room for a computation covering 365 days.
This paper presents one result of an exploratory investigation to derive BTLRF by the use of
Wiener Filter Technique to the heating and cooling load calculated by the U. S. Post Office Energy
Analysis Computer Program,
The BTLRF were found to be dependent on time if they were to be applicable for the calculation
of hourly building thermal load over as long as a half year's period. This consideration is necessary
because building thermal load characteristics cannot be considered stationary if the time span is as
long as a half year.
The time span of the hourly data used to determine the BTLRF was 336 hours for the calculation
illustrated in this report, although it could most possibly have been shortened to 168 hours or even
less, A satisfactory length of the filter appeared to be 4 terms (j =0, 1, 2, 3).
Although BTLRF provide a relatively good estimate in load calculation by a very simple algebraic
operation, the coefficients obtained by the Wiener filtering technique did not follow the expected
trend that the absolute value would eventually start decreasing steadily. Further work is being per-
formed at the Environmental Engineering Section of the National Bureau of Standards to obtain building
thermal load response factors which do follow this expected trend and which are therefore more amenable
to physical interpretation.
5, References
[1] U. S. Post Office Department Report "Computer Program for Analysis of Energy Utilization in
Postal Facilities", Copies obtainable from J, M. Anders of the U. S. Post Office Department,
Washington, D. C. , .
[2] E. A. Robinson, Multi-channel Time Series Analysis with Digital Computer Programs, Holden-Day,
San Francisco, , p. 249.
[3] T. Kusuda, "Thermal Response Factors for Multi-layer Structures of Various Heat Conduction
Systems", ASHRAE Transactions, pp. 246-271, , Chicago, Illinois,
121
■J
Dry-bulb Temperature, P
Solar Energy, Btu per 3q.ft,hr
I 1
J
J
}
Internal Heat Generation, Btu per hr
J L
■ r~i .
48
Men Tue
96
Wed Thu
144
Prl Sat
Hours
192
Sun Mon
240 288
Tue Wed Thu
Figure 1. Excitation functions used for the thermal load calculation by USPOD computer program for the
first two weeks of January.
122
-
-
^-
QQ
Q-
a:
o
_j
CD-
en
>-
_i
ZD
O
WfiSHINGTON. 0. C
JflNUflRY 1-7.
-500
0
500
100[|
o
a B
□
□
i a
■
g B
I
g : i i ; i s ^ §
° ° ° ■= B S B i °
° =. ° B ^ ° a
□
□ B
O
ID 8
□ S
□
□ Q
□ Ip
ID
15 20 25 30 35
DRY BULB TEMPERniURE, F
40
Figure 2. Relationship between the calculated hourly thermal load and outdoor air dry-bulb temperature.
123
Q
cr
o
CD
en
LU
>-
_j
en
ZD
o
•
■
-500
0
500
WRSHINGTON, D- C, JflNURRY 1-7,
0
a o a
%
o
a
o «
a o ° o °
B a
Q Q
20 40 60 80
SOLAR HERT, BTU/HR. SO. FT.
100
Figure 3- Relationship between the calculated hourly thermal load and solar radiation over the south
facing wall.
124
1/nte 'awn nvraiaHi
125
126
Thermal studies by
electrical simulation.
Application example to the study
of the heating equipment of an
apartment building heated by electricity.
J. Anquez and L. Bertolo
Centre Scientifique at Technique du BS.tiraent
Paris - Prance
For the study of- trasient heat flow problems we dispose of a
simulateur composed of an electrical model with resistors ant capaci-
tors, a direct current analog computer fitted with a logical console
and the necessary input and output devices.
The electrical model allows to represent a group of three rooms.
The time contraction on this model is in the ratio of 0,2 second for
24 hours.
The direct current analog computer allows to :
- feed on the model the climatic or occupancy data,
- represent heating and its control.
The input device allows to store for instance the climatic or
occupancy data throughout an entire heating season.
The output device includes a fast recorder and a group of digital
counters allowing an analysis of resuits.
The following problems can be treated :
In artificial climatization (heating or summer air conditionning) :
- Studies on the power required in the course of sequences of the
hottest or coldest day.
- Studies on the consumption in the course of a season of heating or
air conditionning.
- Studies on the efficiency of a control system during typical sequence
of several days or months.
In natural climatization :
- Studies on the variation of the interior temperature in a room during
typical sequence of several days or months.
- Studies on the frequency curve of the temperature in a room throughout
a season.
As an exqmple are given some results relating to the study of the
heating device in an partment building heated by electricity.
The heating system selected for the study includes a base heating
by storage in the solid concrete floors where the energy is supplied
principally during the night hours and a additional forced air heating
which is controlled by a thermostat in each room.
We have studied the influence of the heating device and its con-
trol on the comfort condition and the energy for heating (base tem-
perature, power capacities, etcetera).
127
Key Words : Electric heating, accumulation
heating in the floor, blowed air heating,
consumptions, power, control, comfort.
1 , Introduction
To solve conduction heat transfer problems in vmsteady state conditions we make
use of an analog method to represent thermal characteristics of walls and floors by
networks of resistors and capacitors. The simulator we have developed on this basis
is specially suited for buildings problems. Below we give a brief description of this
simulator and as an example the study for the electrically heated system of an apartment
building.
2, Description of the simulator
The simulator is composed of three basic section :
- RC network
- a direct current analog computer fitted with a Logical console,
- the data input and output devices.
The photograph of figure 1 shows the overall view of the simulator and also indi-
cates names of the major components of all the sections described below.
2.1, RC network
The model is based on the analogy between heat transfer in wall having thermal
infertia and propagation of electricity in a circuit having distributed resistance and
capacitance. In pratice it is difficult to design such an electric medi-um. So the
distributed constalit equivalent circuit representating a wall is obtained by combining
quadripoles in serie, each of them representing a slice of the equivalent circuit,
therefore a layer of the wall.
To determine the thickness of the slices, the heat transfer of a sinusoidal signal
in an homogeneous wall has been stiidied. The mathematical resolution of this problem
being known, it is possible to calculate the temperature and the heat flux in each plane
parallel to the faces of the wall. It is also possible to calculate, for the same signal,
the temperature and the heat flux at the interface of each section of the lumped circuit
equivalent wall. By comparing these two calculations the error introduced by the slicing
is determined ; this error is mainly a function of the frequency of the signal. Thus,
knowing the highest frequency present in the problem and the acceptable error, the
thickness of each slice can be determined. In case the highest frequencies present in
the problem are introduced a on-off thermostat for instance (the cycle of the tran-
sient phenomenon being of the order of fractional hour) and with an acceptable error of
on per cent, the thickness of the slice must be about one centimeter. Thus it requires a
great number of slices. Still hight frequency signals transmitted through the wall are
quickly damped, and it is not necessary to keep the same slicing over all the thickness.
In practise, after four of the thinest slices, it is possible to double the thickness and
so on.
To al].ow an easier operation, fifty walls, each one including six sections have been
prewired, thus the coupling between plug-in type resistors and capacitors were ma.de once
for all.
The surface resistances network in a room is also pre-wired. In this network the
convective heat transfer between each wall and air and the radiative heat transfer from
each wall to the others have been distinguished. Three networks, allowings to represent a
group of three rooms, are pre-wired in this way. The value of the convection coefficients
on the horizontal walls changing with the sense of the heat flux, these coefficients
are represented in the model by circuits of the type shown on figure 2.
The ratio of electrical time to thermal time used in the model being of the order
of 2 to 4 X 10-D, the duration of one day is 0.2 to 0.4 second. The ratio of electrical
resistance to thermal resistance is of the order of 10-6 ohms for 1°C W-^but can be chan-
ged. Taking into accoxmt the time ratio above, the ratio of electrical capacitance to
thermal capacity is of the order of 2 to 4.10-6yU.F for 1 J°0-K
128
2.2, The direct current analog computer.
Fifty operational amplifiers are used to perform the following fvinctions :
- Impedance matching of the generators supplying the clims.tic and occupancy data. to the
network and also impedance matching of the network to the device recording the voltage
at several nodes.
- Data summation : for instance summation versus time of voltages representing outside
temperature and solar radiation on a wall to obtain a voltage representing sol-air
temperature.
- Current generators ; for instance current generator representing solar heat flux
entering in a room by openings.
- Representation of heating, air conditionning control systems.
The logical console is composed of logical modules (AND, OR, NOR, NAND, comparators
etcetera) and electromechanical relays or electronic switches, this system, supplied
with pulses or square signals recorded on the input device (magnetic recorder) described
in the section below, allows to control at predetermined times the following functions,
for instance :
- generation of a heat supplied by the heating or air conditionning equipment or by the
occupancy,
- change of a ventilation rate.
2,5, Data input and output devices.
The data input device is composed of a punched tape reader, a digital to analog
converter and a fourteen tracks magnetic tape recorder. Each climatic data is recorded
on a punched tape in fifteen minutes steps. The same operation is made for the occupancy
data if they are functions of the time only. During the reading of the punched tape the
digital data is converted to analog signal and recorded on a track of the magnetic tape.
All the data relating to a building in a given locality outside dry bulb temperature-, so
lar radiation on the walls, humidity rates of the outside air, etcetera, are stored in
this manner.
Two output devices can be used. The first one is a twelve tracks ultraviolet photo-
graphic recorder fitted with two types of galvanometers ; the three decibels bandpass of
which are four hundred of fifteen hundred cycles per second respectively. The second one
is a system of digital counters allowing an analysis of the results ; consumption state-
ments, statements of the number of times a temperature is reached or exceded, etcetera.
3, Scope of the simulator.
The design of the simulator has been made to match at best the study of the follo-
wing problems :
3.1, Natujal climatization.
- study on the variation of room temperature during a typical hot or cold spell, for
instance.
- study on the variation of temperature in a room throughout a heating or cooling season
In such a case, real climatic data of a given locality are used and the maximum daily
temperatures frequency curve, or the curve giving the total time during which the tempe-
rature stays at a given value may be determined.
3.2, Artifical climatization
(heating or summer air conditionning)
- Analysis of the power required in a room throughout the coldest or hottest days
sequences, to determine the heating or air conditionning equipment.
- Analysis of the power consumption in a room throughout an entire heating or air
conditionning season, to determine the energy requirement or the frequency curves of the
room temperature (air temperatxire , floor temperature in the case of floor heating or the
air relative humidity in humidifying climatization systems, for instance),
- Analysis of the efficiency of a control system throughout the season or a sequenc
of clear but sunny days in mid-season heating. The efficiency of the control system may
be judged by taking into account the energy requirement and comfort conditions obtained
by the system.
129
4, Stiidy of the heating device of
an apartment building heated by electricity
Reported here is a study of a heating device of an apartment building, the power
source being electricity'
The building had a large thermal inertia and a good thermal insulation.
The system analyzed includes :
- A base heating by storage in the solid concrete floors, the power being supplied
principally during the night hours.
- An additional forced air heating controlled in each room by a thermostat. The air taken
from outside, is pre-heated to a temperature Tp before supplied to the room ; this prin-
cipally is to allow sufficient amount of humidifi cation is neoassary.
The heating system and its control system (capacities, base and preheating tempera-
tures, ...) were studied to determine the best balance comfort conditions - energy consum-
ption.
4.1, Climatic data
Prom the records obtained by the national Meteorology Office in Le Bourget station,
near Paris, we have chosen two sequences (Fig 3) :
1^"*^ sequence (february . 15 th to 28 th)
this is a typical sequence of cold and sunny days, the outside air mean temperature being
near the base temperature of the place (- T°C) for several days.
2^*^ sequence (march 29 th to april 11 th, )
this is a typical raid season sequence, the outside air mean temperature being rather high,
the diurnal variation and the direct solar radiation being also higho
For these two sequences :
- The outside air temperature is the real one recorded in the station.
- The solar radiation has been computed by means of the curves giving the intensities of
the direct normal radiation and of the diffuse radiation on an horizontal plane with clear
atmosphere, of the sunshine hours and of the cloud cover factor. The shading effect crea-
ted by the balcony has been taken into account.
- The long wave radiative exchange balance is a linear approximation of the following for-
mula :
B = a u(4-©'3 )
b : heat balance (W m~^ )
a : absorption coefficient of the wall
0s ^nd Tre : respectivelv wall surface temnerature and environment radiant temperature
(°K) " _o _4
^0 : Stefan - Boltzmann constant (W m " ° K )
Tre is approximated only as a function of the cloud cover factor. We have, for a
vertical wall :
Tre - Tae - 2^0 for a cloud cover factor greater than 3
Tre = Tae - 6°C for a cloud cover factor lower or equal to 3,
(cloud cover factor is in the range of 0 to 8)
Tae being the outside temperature.
4.2, Description and characteristics of the studied rooms (fig. 4)
The building includes about 200 apartments of a single surface exposure. It has a
symmetry plane parallel to the facades and its orientation is E.W.
We consider a slice of the building bo-unded on two sides by the west frontage and
the symetry plane and on the other sides by the adjacent rooms.
We assume that the slice being studied and the adjacent ones have the same operation
characteristics therefore, the same inside conditions.
1, Inside Wall OomDOSition (1)
- Horizontal walls : they are made of heavy aggregates solid concrete, 15 cm thick ;
the floor can be covered with a velvet pile with or whitout coarse haire cloth.
130
- Vertical walls : they are either of heavy aggregates solid concrete 15 cm thick as the
horizontal walls or, plaster slabs 7 cm thick.
2, Fagade Composition
The faQade panel is of the light type. Its mean thermal transmission coefficient K is
1 .68 W m-2 oc-1 . m
The opening is fitted with double glazed windows (1), externally screened by shut-
ters and internally by a light-coloured blind.
The shutters are always closed during night from 9 p.m. to 8 a.m. and on occasions
during the day. The opening thermal transmission coefficient is dependent of the position
of the shutters : o i
Shutters open : K = 3 W m "C"' .
Shutters closed : K = 2.4 W m-2 OQ"'
3, Occupancy
The heat generated by the bed-room occupancy has been fixed at 90 W from 9 p.m. to 8 a.
next morning.
4. Exchange coefficients.
The radiative exchange coefficients were calculated by the standart formulas while the
convection exchange assumed the following values :
- Vertical walls : 5-4. W m-2 _2 _^
- Horizontal walls, upward flux : 6.3 W m~ °C ^
- Horizontal walls, downward flux : 0.6. W m~2 oc~
4.3, The heating device (Fig 4 bis)
1 , A preheating of the force circuDated ventilation air to a temperature Tp,
The primary purpose this preheating is to be able to maintain the water content in the
ventilation air above 6 g for 1 kg of dry air. The forced air rate is constant at
30 m3 h-1 .
2, A base heating by a cable embelled in the concrete floors allowing a storage. The
energization of the embelled heater is made during the off peak usage hours, at the maxi-
mum during night hours. Heating and preheating alone vould give a mean temperature Tf
of 10 to 18°C according to the time of the heating season taken into consideration.
3, A supplementary heater installed in the air supply system to the individual room
complements the base heater system to provides 20 +o 22 °C with a control thermostat in
each room (thermostat threshold ± 0,5°C, response time 10 minutes).
The power capacity of this supplementary heater is fixed at 500 w, much higher than
the room needs, to take into account losses by the adjacent rooms and to allow a greater
flexibility to the heating system.
The air is exhaused in the passage-room, where the heat losses by the adjacent rooms
and to allow a greater flexibility to the heating system.
The air is exhaused in the passage-room, where the heat loss from the forced air sup-
ply duct is taken into account.
The power consumpted in the supplementary heater can be billed individually and its
rate structure is different from that of the base heating, which is billed collectively.
4.4, Results
The control system of the base floor heating is an open-loop system (no feedback
from the air temperatures obtained inside). The night hours are divided in a number of
equal intervals of time. In each of these intervals the connection of the heating resis-
tances is commended in such a way that the ratio time of connection is a function f
length of interval
(0 ^ f ^ 1 ) of outside weather parameters : this is approximately equivalent to supply
continuously a heat power ^ equal to f. ( | = installed power).
131
Here we limit ourselves to the comparison of two control systems :
- one taking into account the instantaneous value of the outside temperature during the
time when the baseheating system is energized,
- the other including the mean values of the outside temperature and the solar radiation
on the room facade.
The comparison will made on the max:i miun temperatTxres attained in the room and on the
energy consumption.
We will consider only the case where the power is supplied to the floor heater dixring
night hours, that is to say from 10 p.m. to 6 a.m.
a, Control from the instantaneous
value of the outside air temperature,,
Assume first that the power heat supplied to the base floor heater was controlled to
the following expension :
f (t) = Tf (t) - k2 Tae (t) - k3 Tp (t) (2)
- Coefficients k1 , k2, k3 are defined as functions of the thermal characteristics of the
room and those of the heating and ventilating equipment.
- The preheating is set on a particular temperature Tpo :
if T i T , T = T
ae po ' p po
if T > T , T = T
ae / po ' p ae
The resTxlts which are presented are those obtained when the preheating is not swit-
ched off during the peak hours.
From the first it is know that the control mode cannot be satisfactory, on the one
hand because it does not take into account the solar radiation contribution and on the
other hand, because the outside air mean temperature measured between 10 p.m. and 6 a.m.
may be quite different from that of the day. This leads to a base temperature drift, this
drift becomes more significant as the preheating is low and the diurnal variation of air
temperature becomes large.
During the february sequence, this drift is very low, as shown on the air temperature
records of figure 5 where the base heating is working alone. Otherwise it is of about 2,5''(
at the end of the april sequence, for Tf = 16°C and Tp = 6°C, where the solar contribu-
tion are not taken into account by the control ; this drift is increased due to the fact
that hight solar heat gain are coincident with hight diurnal variation of the outside
temperature.
Minimization of this drift is possible only by lowering the base temperature during
mid season.
Figures 6,7 and 8 show the inside air temperature when the thermostat is set at 200C«
In february, and in the case the solar, contribution in the room is less important
because of balcony structure, the inside temperature, 21 °C mean value, is still acceptable
for a base temperature of 16°C, preheating to a temperature greater than 6°C improves the
comfort conditions (air and floor surface temperatures in the morning) and lowers very
appreciably heating energy requirement during the night hours ; so when Tf = 16°C, Te =
- 5°C and if 22°C inside temperature is wanted by heating dxuring the off peak hours, one
must have ;
if T = 6°C : Power capacity = W
P floor = 25.5°C
ceiling = 30°C
if T = 16°C : Power capacity = W
P floor = 24.2. °C
ceiling = 27,5°C
At the end of the april sequence and for Tf = 14°C, are still recorded very incom-
fortable air temperatures, of the order of about 240C mean value (without balcony). In
132
fact, windows woiild be opened to restore more acceptable comfort conditions, but the
consumption waste would be increased.
b, Control from mean outside
air temperature and solar
radiation.
The heat flux supplied is of the form :
T ' 1 f-t-t2 f t-t4
$ t = (Tf )t - t2ltr" I Tae d © - k6 (Tae)t - k7 t4ltT~ ^ ^
/t-t1 /t-t3
- k8 (Tp)t
- The time intervals t^ - t2and t^ - t- being included in a cycle which may be daily.
- Coefficient k^to kg are defined as functions of the thermal characteristics of the
room and those of the heating and ventilating equipment.
- R is the solar radiation on the fagade.
- Tp is defined as in 4.4, a, but the preheating is switched off during the peak hours.
The improvement attained by this type of regulation over the former one is very dis-
tinct for the april mid-season sequence.
On the fig. 9 some results are reproduced, the base heating working alone, with and
without controls taking into acco-unt the solar . radiation .
- In case the controls does not take into account the solar radiation, the drift is sligh-
tly greater than 0,5°C at the end of the sequence with solar factor zero and,
- In the case the controls takes into account the solar radiation, the drift stays sensi-
bly in a bracket of + 0,5°C.
On figures 10 and 11 one can read the inside air temperature variation for different
values of Tf, the thermostat being set at 20°C.
At the end of the april sequence, heat gain from the solar and occupancy contributions
are greater than the losses ("Tf being between 10 and 16°C), inside air temperature does
not change much, staying in mean value around 21 to 22°C, the peaks not exceeding 24 °C,
The difference is much significant in relation to the relative values of the power
consumed ; with a balcony in the case corresponding to figures 10 and 11, the consump-
tions recorded during the fourteen last days for base and supplementary heatings are the
following :
T _ igoc ( ^ase : 60 kWh
f (Supplementary : 8.1 kWh
T - mop (Base : 22.1 kWh
- lu I. (Supplementary : 48.9. kWh
For comparison with the control scherae defined in 4.4, a, the energy requirement
recorded in the some conditions are :
T _ (Base : 82 kWh
^ ~ (Supplementary : 4 kWh
The results for the february sequence are given in fig. 12.
5, References
(l) The thermal characteristics of the
building walls (thermal conductivity, mass
per unit surface, K coefficient, etcetera)
are extracted from the Docujnent Technique
Unifie : "Computation riiles for the servi-
ceable thermal characteristics of the
building walls and off the basic losses
of the buildings".
133
1
m
rM -P
CO C
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a -H
O O
N -H •
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0) O
O O (1) iH
W CD O -P
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a1Q
40
Double glazed
window
130
80
250
Figure 4 , Studied Rooms and Facade Drawings
136
outdoor porometerp
outdoor Gir
Tp
Preheating contro
versus humidit/
control
Box
commutotion Box
embedded cables
Control in on
■r^ff thf»rmn<;tnt
t
Supplementary heating
Ti
^
Figu.re 4bis - System schematic
137
FEBRUARY With Loggia Tj= 16°C
to
17
Tp 3 6*te
7
APRIL With Loggia T| = 16 C
Tp o 6"C 16
Pigure 5, Inside Air Temperat\ire.
Base heating only, regulated as a ftmction
of the outside air temnerature.
138
Figure 6, Inside Air Temperature. Base heating regulated
as a function of outside air temperature. Additional heating
thermostat setting : 20 °C
139
FEBRUARY With Loggia Tps.lft^C
If.
Figure 7j Inside Air Temperature. Base heating regulated
as a function of outside air temperature. Additional heating
thermostat setting : 20°C
140
FEBRUARY Without loggia Tp= 16 °C
IOC
21
16<»C 20
19
22.
27
OA
\J
\
1
23
J
i
7
Figure 8, Inside Air Temperature. Base heating regulated
as a fiinction of outside air temperature. Additional heating
thermostat setting : 20°C
141
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146
Analog Computer Simulation of an Air
Conditioning System in a Commercial
Building Incorporating Yearly Weather
Data
John L. Magnussen 1
Honeywell Inc.
Estimated operating costs of various air-conditioning systems is an
important economic consideration in the design and selection of equipment
for a new building. Building construction, the heating/cooling system and
the controls must all be considered to minimize these operating costs and
provide comfort control. To analytically accomplish this task, a small com-
mercial building was simulated on an analog computer so that the building
orientation, construction and number of zones could be easily varied. Yearly
weather data for various U.S. cities was programmed on a 13-channel tape re-
corder according to recommended ASHRAE procedures to simulate realistic en-
vironmental conditions. Programming the analog computer for various heating/
cooling plants and control systems provides a quick analysis of initial cost,
operating cost and comfort performance.
Key Words: Analog, control system, digital, heat transfer, modeling,
simulation, solar radiation, system analysis, thermal capacity.
1. Introduction
Company sales and profitability can be significantly affected by employees' working environ-
ment. Maintaining the optimum environment at the least cost should yield increased productivity
and higher profits. The main factors influencing operating cost and thermal comfort are the
building's construction, location and orientation, the heating/cooling system and the control
system. To analyze all these factors creates a complex problem requiring special tools such as
analog and digital computers. Specifically, analog computers provide the dynamic results essential
to complete analysis of control system stability and performance. The analog computer can simulate
an actual heating/cooling system and illustrate the anticipated performance under various environ-
mental conditions, building construction and controls. Cost performance data may be graphically
displayed in real time, permitting rapid dissemination and comparisons of various systems.
An optimum environmental system maintains a comfortable environment at the lowest operating
cost. This paper shall present a method for analytically determining system operating costs. The
method utilizes an analog computer simulation of a small commercial building. Cost and performance
data from this simulation are then used to accurately define optimum system performance.
2. Cost Analysis
Heating/cooling system costs are composed of initial cost, operating cost and maintenance cost.
Generally initial cost includes hardv;are such as the compressor, condenser, furnace, boiler, duct
work, piping, controls, etc., plus the cost of system installation. Once the system is installed, how-
ever, operating and maintenance costs are the main concern of the ovmer. This paper will be limited
to determining the operating costs.
The financial return of a building is highly dependent on the efficient operation of the heating/
cooling system. In dollars, this means the lowest possible total energy consumption necessary to
maintain comfort conditions. Operating costs are generally those derived from operation of the
condenser fan, delivery system, furnace and controls.
Senior Development Engineer, Residential Division.
147
An accurate calculation of yearly heating/cooling operation can be a simple summation of the
heating/cooling plant's operating time if it is strictly on/off. If a modulating system is used, inte-
gration of the heat/cool delivered energy must be made. The energy requirements, together with the
efficiency of the heating/cooling plant, can predict fuel consumption. Efficiency defined as the ratio
of output in BTU/hr. to input energy provides a functional relationship (between energy required and
energy consumed) to incorporate into the simulated system. System operation can then be calculated
since the system is responsive to the outdoor conditions affecting efficiency, such as dry-bulb temper-
ature (for an air cooled condenser) and wet-bulb temperature (for water cooling towers). All of these
calculations may be made with an analog computer.
Numerous authors have proclaimed the advantages of computers, particularly in comparison to field
testing. For to rely on field testing only leads to added costs, development delays and inaccurate
results because of an uncontrollable environment. A computer-aided design, however, enjoys the
benefits of a controllable environment, accurate definition of the effects of a single variable,
accurately defined results and hence lower total development costs.
Of particular concern in determining operating cost is the solution of dynamic problems. An
analog computer was selected for this analysis because of the ease of simulating the transient be-
havior of a heating/cooling system and the inherent dynamic problem solving ability.
The analog computer complements the passive electrical circuit simulating thermal properties of
the small commercial building, automatically incorporating nonlinearities involved in total system
analysis. It thereby completely calculates the transient behavior of the heating/cooling system as
the system responds to demands of the conditioned space, created by anticipated internal as well as
external environment loads. For the simulation, the external environment was modeled using data from
the U.S. Weather Bureau.
The simulated commercial building is a 90' x 30' structure, 8' in height per story with a slab
floor and a flat ceiling. Exterior walls are all opaque material, 50% opaque and 50% transparent, or
all transparent. A floor may be divided up to 12 separate areas, each 15' on a side, to create
separate 225 sq. ft. zones. An analysis of a multiple story building may be made by rerunning the
simulation with appropriate adjustments for the thermal inputs to the floor and ceiling, changing the
thermal characteristics of the floor and ceiling, and eliminating all heat flow between stories by
assuming the same control temperature for all floor sections. Thus the structure of the building, the
number of zones and the type of exterior walls all may be varied.
The analysis of dynamic control performance and operating costs requires that the simulation in-
clude all thermal characteristics of the structure. Therefore all three modes of heat transfer -
conduction, convection, radiation, and the thermal capacity of the structure must be included in the
simulation. However, a given wall, floor or ceiling can never be perfectly simulated to produce an
exact duplicate of the temperature profiles in the structure or the heat transferred. Therefore
assumptions are needed to bring the problem within the practical capability of present-day techniques
and technologies and be solvable with a realistic expenditure of funds.
In this simulation the lumped nodal point method of analysis was used. This analysis assumes
that for each wall, a uniform temperature is maintained on any surface, the wall is of uniform con-
struction, and it has a linear temperature gradient between any two surfaces.
In an actual installation heat does not flow in a straight path through the wall but rather flows
along the path of least resistance. There is also a discontinuity between wall material surfaces.
In this simulation a single temperature is assumed for the active wall and an average discontinuity is
assumed between any two members (i.e. a uniform discontinuity is assumed between the studs and the
plasterboard that is fastened to the studs). Assuming an average discontinuity an average thermal
contact resistance may be calculated. The thermal contact resistance is the resistance to heat trans-
fer between two items fastened together.
From past experience, these assumptions should present a deviation less than 10 per cent between
actual and predicted heat flow characteristics of the wall, so that the dynamic effects on analysis
and total energy loss will be minimized. The anticipated difference is further minimized by using
one "T" section for each wall material and then building up the several "T" sections for an entire
wall (as shown in Figure 2) rather than just one "T" for the entire wall. The equation:
3.
Computer Design of Temperature Control Systems
Simulated Commercial Building
148
(where 1 = thickness of material to be treated by one "T" section for an accuracy of 5Z, ft. a =
thermal dif f usivity , ft^/hr., f = frequency of the disturbance, cph), may be used to define the maxi-
mum allowable thickness of material that may be represented by a single "T" to achieve a maximum
deviation of 5% in a 24 hour variation of temperature (i.e. as would occur over an entire day). For
example, plasterboard may be 4" thick before more than one "T" is required to prevent a 5% deviation
of the response of an oscillating heat flow through the plasterboard.
The electrical circuit to model one zone (Figure 1) includes resistive elements representing heat
transfer due to radiation between the walls, floor and ceiling, convection heat transfer between the
room air and the walls, floor and ceiling, and conductive heat transfer through the walls, floor and
ceiling. Figure 1 also shows the heat transmitted through the windows (this element is removed if
glass is not present) and the capacitive elements simulate heat storage in the room air and walls,
floor and ceiling. For a typical exterior wall (Figure 2) the resistive elements represent heat
conduction through the various portions of the wall and capacitors represent the heat storage of
these parts. Values of resistors and capacitors are dependent upon the scaling used to model the
structure. For this simulation the dynamic effects occurring during 24 hours of actual time are cal-
culated in 14.4 seconds.
Air movement between sections is simulated by adding a special resistive network to the basic
circuit (Figure 1). The resistance network is connected to points representing room air temperature.
Thermal capacitance of each air space is represented by a single capacitor.
Figures 3 and 4 show the cabinet that contains the physical circuitry used to make this simulation.
The resistors and capacitors that form the "T" sections shown in Figure 2 are placed in a plug-in con-
tainer. One container is used for each wall section (i.e. the container for an interior wall would in-
clude the resistors and capacitors for an 8' x 15' area). These containers are visible on the front of
the cabinet (Figure 3). The containers on the lower panel of the cabinet are for the walls and win-
dows; above these are the containers for the floor and ceiling sections. These containers may be easily
changed so that different types of wall construction may be simulated. For example, if concrete blocks
were used instead of brick and plaster on the exterior walls, the exterior wall containers would be
changed to those that include the resistor and capacitors sized for a concrete block wall. Since
these are plug-in containers, changes can be made quickly and the analysis continued to determine
the effects of the new wall construction.
5. The Simulated External Environment
To calculate the annual cost of operating a heating/cooling system, the external environment is
simulated using weather data from the U.S. Weather Bureau. Weather variables are changed every hour
to closely approximate actual dynamic changes. Ten years of data are contained on a single reel of
magnetic tape. The data are provided in a digital form from which the characteristics pertinent to
the thermal simulation were converted into analog signals and recorded on an analog magnetic tape.
Environmental factors used were dry- and wet-bulb temperatures, relative humidity, wind velocity
and direction and solar radiation. Hourly values for the factors necessary to calculate the solar
radiation (cloud type and height, amount of cloud cover and the time of day and day of the year) were
read from the Weather Bureau's digital magnetic tape and then used according to ASHRAE procedures
outlined by the Task Group on Energy Requirements, providing a programmed method of calculating both
direct and diffuse solar radiation intensities for any wall. Additional statements were added to
the digital computer program to read information from the Weather Bureau's digital tape. The re-
sulting digital computer program read and calculated values for the solar radiation intensities and
5 other pertinent environmental factors. A total of 13 variables - dry- and wet-bulb temperature,
relative humidity, wind velocity and direction, the year, hour and week, solar radiation intensities
for an east- west- north- and south- facing wall, and a direct normal radiation intensity were
either calculated or read from the digital weather data tape. Hourly values for a 4-year period for
these 13 variables were then recorded on a 13-channel analog magnetic tape. The analog tape is an
FM recording, although the output from the tape recorder is a voltage or analog signal. The outdoor
ambient temperature, reproduced as an analog or voltage signal, is connected to the appropriate
points of the electrical circuit (Figure 1). Since solar radiation intensities are directionally
oriented, the simulated building may be oriented in any direction by simply changing analog signals
in the cabinet (Figure 3).
Inside the cabinet (Figure 4) is the pull-out printed circuit board on the right hand side which
contains all the interior radiation and convection heat paths. Figure 5 illustrates the board used
for the one zone application. The six panels near the bottom of the cabinet (Figure 4) contain the
resistive, capacitive network that simulates the heat transfer through the ground. Points from this
circuit are connected to the underside of the building's slab floor. This two-dimensional circuit
effectively simulates heat transfer to 16' where typically only 5% of the yearly outdoor ambient tem-
perature oscillation is found. The circuit automatically provides for the complex heat loss from the
building to outdoor ambient conditions through the earth by incorporating the dynamic nonlinear effects
149
of the ground, effects that would otherwise be next to impossible to solve by either digital or
analytical solutions.
Air infiltration is accounted for by a direct heat transfer path between each point representing
the space temperature for a 225 sq. ft. area and an equivalent outdoor ambient temperature, simulated
by a representative resistance. Wind velocity defines the value of the equivalent outdoor ambient
temperature. Special analog circuits to achieve the correct direction for air flow and duplicate
wind direction heat gain or loss,
6. Simulation of the Heating/cooling System
Analog simulation of the building structure combined with the heating/cooling plant provides a
system approach to analyzing the complete control loop (Figure 6). To simulate the heating/cooling
system, response characteristics of the physical components — the furnace, conveyance, cooling coils,
— must be known. Once the response characteristics are defined - either by sinusoidal inputs (fre-
quency response method) or step inputs (step response method) - the control loop may be established
(Figure 6).
Furnace time response may be found by measuring plenium air temperature from, a step input,
simulated by a transfer function of the form
, . T/Q = K/( -r s +1)
where T = air temperature rise in the plenum, Q = heat output of the furnace, K = steady state plenum
temperature rise per unit Q, s = the Laplace operator, and = the single order time constant charac-
teristic of the furnace. Various types of furnaces - electric, gas, oil, coal, etc., may be modeled
using different time constants ('?'), Radiant panels or baseboard heaters may be simulated by
similar transfer functions, but with heat added directly to the ceiling surfaces for radiant panels
and to the walls and floors in addition to the air for baseboard heaters.
The cooling plant may be modeled similarly with the extent or complexity of the simulation
depending on the type of plant used, i.e., cap tube, absorption, reciprocating or centrifugal
chiller. Since the sensible-latent heat removal relationship is continually varying, the dynamics
of operation are more complex than the furnace simulation. Latent heating effects are necessarily
included to calculate realistic operating costs, since the efficiency of the air-conditioning unit
is dependent not only on the outdoor ambient conditions but also on the latent heat load across the
cooling coils. The latent heat introduced by infiltration of outdoor air as well as that generated
by occupants must be considered.
Transient moisture storage of various materials found in typical furnishings was based on actual
field measurements of step-response tests from a humidity source. The data obtained from these tests
defined the transfer functions used in the computer simulation. Dry-bulb and relative-humidity sensors
were modeled and added to the control system circuit through appropriate transfer functions, taking
into account the respective time constants. If an Air Economizer provides free cooling by outside
air, another block must be added in Figure 6 and additional circuitry added to the simulation.
The heating and cooling conveyance, if present, should also be modeled because its relative time
response may be significant to that of the total system, depending on its bcation and the time con-
stants of other system components. A typical metal duct transfer function might be a lead-lag term
such as
Tg/Ti = K ( -PjT s+l)/( -^s +1)
where Tq = outlet temperature rise, T-j^ = plenum temperature rise or duct inlet temperature rise, K =
steady state ratio of Tq/Tj^, = lead time constant, and "2^ = lag time constant. The time constants
reflect the relative duct length and the heat exchange between the air, the duct and the environment.
Last is modeling the control system. A simple on/off control is shown in the control loop
(Figure 6). The basic control system consists of a sensor to detect the current state or condition
a logic device to differentiate what is sensed from a preset or desired condition, and an actuator to
trigger desired action from the appropriate equipment after receiving a command signal from the logic
device. Various auxiliary control components may be added to this basic model as demanded by the
application. Controls simulated may be electric, electronic, pneumatic, fluidic, mechanical or any
combination.
150
7. Computer Operation and Data Acquisition
The computer combines t;he simulated heating/cooling system with the commercial building in a con-
trol loop with the external environment provided by the taped weather data. Since these data form
the load on an unoccupied building, occupancy effects were added separately.
Solar radiation intensity adds heat to the structure. Since current is analogous to heat in the
simulation, the voltage signal from the weather data tape must be transformed into current. These
current signals are then sent to the simulated building by connecting to the appropriate point in the
simulated circuit using special analog current generators. Distribution of this absorbed heat (or
current) is proportional to the voltages supplied from the taped weather data. Separate current
generators are used for the roof and each side of the building and to simulate heat transmitted
through the glass windows.
The voltage signal from the tape recorder representing the solar radiation intensity is a combi-
nation of direct and diffuse components, adjusted to account for average transmissivity or absorp-
tivity of incident surfaces. This is obtained by time-averaging values for each direction (north,
south, east, west, or perpendicular to the earth). This averaging tends to smooth the daily cyclic
pattern somewhat; however, the difference between hourly changes and average transmitted heat is
always less than 10% for any given day.
Sensible heating effects of lighting and occupancy in each zone are accounted for by injecting
convective and radiant heat into the simulated structure at the point that represents the room air
temperature and surrounding surfaces of the particular zone in question.
Output data is recorded by several instruments: A digital voltmeter with BCD (binary-coded
decimal) output capability, a counter timer with BCD output, an 8-channel oscilloscope, an X-Y plotter
or an analog tape recorder. In the present case a counter timer recorded yearly operating costs by
integrating total on time of an on-off system by pulsing a gate to allow the timer to count on its
internal calibrated time base during the permitted period representing the system on time. If the
system modulates according to demand, the heating/ cooling requirements must be integrated and the
counter is then used to accumulate the number of integrations to a given value.
Dynamic performance of the system was recorded on an oscillosgraph where a graphic representation
of zone air temperature, along with other variables, was obtained, permitting dynamic temperature
swings of the zone to be easily determined. The performance and operational characteristics for a
complete year are obtained in only 87.6 minutes, meaning several building types and various heating/
cooling systems can be examined in a single day.
8. Illustrative Example
For example, consider a single-story single-zone building 30' wide by 5D' long by 8' in height
with no internal walls or partitions, and the thermostat is mounted on one of several support columns.
All exterior walls have plate glass along the top half, opaque material on the bottom half. The
building, located in Houston, is oriented so the long wall faces south.
A simple one-stage heat, one-stage cool system was simulated for the heating/cooling plant. To
this was added a heat/cool space thermostat for control and an Air Economizer to use outside air for
free cooling whenever possible. The Air Economizer has two temperature sensors: One which senses
outdoor air temperature and one which senses combined (or mixed) air temperature obtained from return
air and outside air temperatures. Two setpoints (one for each sensor) let the Air Economizer pull in
outside air when outside dry-bulb temperature is below its setpoint and regulate the amount of outside
air entering through a damper according to the mixed air temperature (channel E, of Figure 7). The
damper responds to loads on the structure and the control setpoint. For the illustration shown, the
mixed air setpoint was 60°F and the outdoor air permit temperature setpoint was 70°F. The minimum
position of the damper was set to provide 10% outside air for ventilation purposes.
Figure 7 presents the typical oscillograph output of such a simulation. The time period shown
is the last 2 days of January and the first day of February, . The two timing channels, D and H,
are identical. Channel H is included only as a reference. Time is recorded in 1-hour steps from mid-
night through 24 hours, then resets. The cyclic pattern of outdoor air temperature, channel A, varies
from day to day. To approximate this pattern with an average condition that would produce the same
response in space air temperature (channel B) would be extremely difficult as would trying to achieve
an average condition for the directional solar radiation intensities displayed by channels I, J, and K
151
The type of cloud cover (if any), the amount of cloud cover, haze in the atmosphere, ground re-
flectivity and sky diffisuivity are accounted for in the values of these solar radiation intensities.
Infiltration effects of outside air are regulated by wind velocity, (channel F) and wind direction,
(channel G). The sharp swings on channel G are because of the scale used for the trace, from due
north through a full rotation of 360 degrees. As the wind direction changes from north to south the
oscillograph pen must traverse approximately one-half the trace. Outdoor relative humidity is
recorded on channel L,
Variations in the cyclic space air temperature swings, channel B, coincide with the cycling rate
of the thermostat and the heating/cooling plant (channel C). These variations are In response to
changes in the internal occupant and lighting load (present from 8 A.M. to 5 P.M.) and to changes in
the outdoor weather conditions.
On time of the heating/cooling plant may be accumulated by a counter-timer to calculate the oper-
ating costs for the time period and system in question. The effect of different components on the
total system operating cost and performance may be easily determined by changing the simulated part
and rerunning the same weather data.
9, Conclusions
With this simulated small commercial building and weather data, yearly system operating costs may
be determined for a number of different types of building construction, composition, orientation,
location and use. A clear concise distinct analysis providing specific information on the effects
of a single variable may be made using analog computation. Effect of a single variable on total
system performance may be readily defined, as may various conceptual control ideas such as using out-
side air for free cooling through an Air Economizer. Multizone and single-zone systems may be read-
ily examined by changing from a 12-zone to a 1-zone structure. The number of zones may be easily
changed. Various systems may be examined not only over long-term but also over short periods. Occu-
pancy and lighting loads, as well as other internal loads, may be readily incorporated and the dynamic
effects examined. Geographical effects of a particular building and system may be determined for any
location in the United States for which a magnetic weather data tape has been produced. The type of
application a given heating/cooling system is to be subjected to may be readily evaluated. The type of
control may be easily changed and the dynamic performance as well as the yearly operational cost result-
ing from the particular control defined. Knowledge of what the optimum control should consist of, and
knowledge that the control parameter values defined are indeed the optimum values, may be graphical^
illustrated with this engineering approach. The information obtained here is not easily obtained using
field tests or other analytical solutions, especially not within a controlled environment that provides
a convenient and economical method of comparison.
152
10. References
II] Victor Paschkis, Periodic Heat Flow in Build-
ing Walls Determined by Electrical Analog
Method (ASHVE Transactions, Vol. 48, ,
p. 75).
[2] T. N. Willcov, et al. Analog Computer
Analysis of Residential Cooling Loads (ASHVE
Transactions, Vol. 60, , p. 505).
[3] H. B. Nottage and G. V. Parmelee, Circuit
Analysis Applied to Load Estimating (ASHVE
Transactions, Vol. 60, , p. 59).
[4] H. B. Nottage and G. C. Parmelee, Circuit
Analysis Applied to Load Estimating, Part II
(ASHAE Transactions, Vol. 61, , p. 125).
[5] Harry Buchberg, Electric Analogue Prediction
of the Thermal Behavior of an Inhabitable
Enclosure (ASHAE Transactions, Vol. 61, ,
p. 339).
[6] Harry Buchberg, Electric Analogue Studies
of Single Walls (ASHAE Transactions, Vol. 62,
, p. 177).
[7] J. L. Threlkeld: Thermal Environmental Engi-
neering (Prentice-Hall, Inc., Englewood
Cliffs, N. J., ).
[8] Shao Ti Hsu, Engineering Heat Transfer, (D.
Van Nostrand Co., Inc., Princeton, N. J.,
).
[9] Handbook of Fundamentals, (ASHRAE, New York,
N. Y., ).
[10] G. P. Mitalas and D. G. Stephenson,
Absorption and Transmission of Thermal
Radiation by Single and Double Glazed
Windows (National Research Council of
Canada, Division of Building Research,
Research Paper No. 173, ).
[11] G. K. Tucker and D. M. Wills, A Simplified
Technique of Control System Engineering
(Minneapolis-Honeywell Regulator Company,
).
[12] William I. Caldwell, Geraldine A. Coon,
Leslie M. Zoss: Frequency Response for
Process Control (McGraw-Hill, ).
[13] Granino A. Korn and Theresa M. Korn,
Electronic Analog Computers (McGraw-Hill,
New York, N. Y., ).
[14] Tyler Stewart Rogers, Thermal Design of
Buildings (John Wiley & Sons, Inc., New
York, N. Y., ).
[15] Lorne W. Nelson, The Analog Computer as a
Product Design Tool (ASHRAE Journal,
November, ).
[16] Met in Lokmanhekim, ed., (Task Group on
Energy Requirements, ASHRAE, New York,
N. Y., ).
153
outside
film concrete studs and plaster
coefficient block insulation board
outside
temperature
-WW^ vAAA— r^AAA-
X
-vVVV
X
inside
wal 1
surface
temperature
Figure 2. External wall simulated thermal circuit
154
155
SET
POINT
THERMOSTAT
SWITCH
ON-OFF ,
OPERATIOIT
HEAT- COOL
PLANT
PLENUM
TEMPERATURE
CONVEYANCE
OUTLET
TEMPERATURE
AIR
SENSOR
TEMPERATURE
SENSOR
TEMPERATURE
(8v
WALL
TEMPERATURE
SIMULATED
COMMERCIAL
BUILDING
WEATHER
FACTORS
ANALOG
CURRENT
GENERATOR
HEAT FLOW
from
OUTLETS
SOLAR
HEAT
FLUX
ANALOG
CURRENT
GENERATOR
SOLAR
RADIATION
ANALOG TAPE
RECORDER
Figure 6. Temperature Control Loop
156
Figure 7: Oscillograph Recording of System Variables
157
channel I
— • — |- 60,000 BTU/hr -
Solar Radiation Intensity - East VJall
■|- 60,000 BTU/hr --|
0 BTU/hr
Solar Radiation Intensity - West Wall
Channel K i" -j" 750,000 BTU/hr
Solar Radiation Intensity - Roof
i Channel L 1 |
- - 90% -j- - - - - - j -- - - Relative Humidity 1
r.i-^—r>-T~^ — "1 ! t '-.^
[ '.
1
- 10% -A — j 4—
■
Figure 7: Continued
158
Experience with a thermal network analysis programme applied
to heat flow in buildings
*
Norman R. Sheridan
University of Queensland, Australia, .
After a brief discussion of the general features of thermal models for buildings, the paper
describes the general purpose network analysis programme that has been modified for use
in building heat flow calculations. The input data includes the dimensions and thermal
properties of the heat flow paths, the building orientation, the solar radiation on a horiz-
ontal plane, the ambient air temperature, the wind velocity and the rate of air infiltration.
Sub-routines allow calculation of variable convective and radiative resistors. Calculated
output includes inside surface temperatures and heat flow into the building interior. As
an example, calculated values of the diurnal and daily heat flows and the maximum wall
temperatures are given for a simple enclosure with walls of various materials and different
thickness. Factors affecting the alignment of the mathematical model with the prototype
are discussed with relation to a simple enclosure. The advantages and limitations of the
method are critically examined and some comparisons made with the van Gorcum matrix
method, which has also been programmed for similar problems. It is concluded that the
mathematical simplicity and the versatility of the general purpose thermal analyser give
considerable advantage for University type research. On the other hand, the long computing
time of this programme is seen as a limiting factor in its use for routine investigations.
Key Words: Air conditioned buildings, building heat flow, lumped parameter network,
optimum insulation, thermal design, thermal model, thermal network analysis.
1. INTRODUCTION
As a thermal shelter, a building acts to reduce the daily temperature range and to permit adjustment
of the temperature level by heating or cooling. Heat flow in the building shell is transient as a result of
the periodic nature of the ambient temperature and the radiation received at the building surface. Thus,
predictions of the thermal performance need to allow for the unsteady flow and to account for the thermal
capacitance of the shell as well as its resistance.
For a naturally ventilated building, the problem is usually one of predicting the inside temperatures,
both of the surface and the air. On the other hand for air conditioned buildings , the net heat flow and
the wall surface temperatures will be needed.
Justification for a detailed thermal study of a building is usually made on economic grounds. For the
naturally ventilated case, the aim may be to decide the cheapest of various alternative ways of reducing
unwanted heat gains. For the air conditioned case, the aim may be to determine the most economical
structural system which will result from the lowest annual cost of owning and operating the building.
The unsteady flow analysis can be extended to cover the case of unsteady energy input into the air
conditioner, such as is the case in the s^olar air conditioned buildings which have been the subject of re-
search at the University of Queensland. Here, the problem is one of distributing the thermal storage be-
tween the solar collecting system, the air conditioning system and the building in the most economical
way.
2 . THERMAL MODELS
Thermally, a building consists of a number of different heat flow paths in parallel, each subjected to
boundary conditions that may vary from path to path. A typical path through a homogeneous wall (Fig. 1)
has distributed capacitance and resistance. It is affected externally by solar radiation, long-wave re-
radiation to the surroundings and convective heat exchange with the ambient temperature and internally by
long -wave radiative exchange within the interior and by convective heat exchange with the room air.
* Reader in Mechanical Engineering.
159
Fig • 1 . Homogeneous wall with boundary conditions
q = (1 - p) R AH.
It is assumed that heat will flow normally
to plane surfaces the dimensions of which are
large compared to the thickness, i.e. the flow
will be one-dimensional. Thus, each plane sur-
face of uniform construction is considered to be a
single path with the same set of boundary
conditions .
a . Boundary Conditions .
Short-wave radiation entering the surface can
be calculated from the insolation on a horiz-
ontal plane, a factor to allow for surface or-
ientation to the sun and the surface reflect-
ance .
(i)
External long-wave radiative exchange will be governed by the usual Stefan-Boltzmann law with the
assumption that some effective or average temperature can be found for the surroundings, T .
4 „ 4,
q -
^^s2^
)
This equation can be modified to the form:
[V
q - 1
T^)
^2^
(ii)
e„ F A(T + TJ(T
2 s2 s 2 s
'+T )
where R^ is a temperature dependent resistance for a particular wall
Convective heat transfer will depend on the film resistance R^
the velocity in the case of forced convection or of temperature in the case of natural convection.
which will in turn be some function of
The tem-
perature difference is between the ambient temperature and the wall temperature. Thus:
T,
q
L2
Rc
(iii)
Internal radiative exchange could be treated as above or alternatively by the matrix equation:
|b| |w| = IbT^^I ... (iv)
[w[ is a matrix of leaving flux densities representing the response,
|bT4| is a matrix with terms of the form ^2 ^2 Tt'^ representing the excitation,
B is a matrix of system properties and is thus the transfer matrix.
2
For some studies, the boundary conditions can be simplified by the sol -air temperature concept.
(The sol -air temperature tg is that temperature of the outdoor air which, in the absence of all radiation
exchanges, will give the same rate of heat entry into the surface as would exist under the combination of
heat exchanges in the model above (Fig. 1). A combined resistance R^^. , with temperature difference
taken to the ambient temperature, is usually used as:
q =
R
^2^ ' r (^s
r
T^) + a R A H =
2 g
-(T^-T2)+aR AH
cr
r(^e-^2^
cr
(v)
These boundary conditions may be available as a continuous record though more usually they will
consist of a time-series with values at one hourly or three hourly intervals.
b. Thermal Response of Heat Transfer Path.
If the convective and radiative resistances can be considered as constants, the response of the sys-
tem to the excitation can be calculated by superposition of the known response to simple components of
the excitation function. Components that have been used are Fourier harmonics,"^ rectangular pulses,^
and triangular pulses.^
Each excitation function is resolved into components. It is sufficient to determine the response of
the system to unit values of the excitation components since, for the assumed linear system, the mag-
nitude of the response will be linearly related to the magnitude of the excitation. The response function
will be determined by adding the components of the response.
Mathematical manipulation can be conveniently handled in matrix form in which a transfer matrix con-
taining fixed properties of the system is post-multiplied by a column matrix of the response variable and
equated to a matrix containing the remaining terms of the heat balance.
Application of this approach depends upon the ability to determine the transfer matrix and/or the unit
response for the distributed parameter conduction path. These methods are detailed elsewhere.
160
Lumped Parameter Approximation.
The conduction path can be. approximated by a lumped parameter network of thermal resistances and
capacitances which gives a finite difference approximation to the partial differential conduction equat-
ion. The one -dimensional heat flow path of building problems is imagined as being divided into a
number of slabs which have their heat capacity concentrated at their midpoints. The path for heat flow
is formed by the thermal resistance of each slab which is lumped to connect appropriate midpoints or
nodes. For a reasonable approximation from 3-5 divisions of each conduction path should be made.^
Heat flows into or out of the path can be made by
I adding or subtracting heat from boundary nodes or
by allowing heat to flow through convective or rad-
iative resistances connected to the boundary nodes.
The interconnected circuit of thermal resistances
and capacitances is the thermal network.
1 ^
"c"
3 . SOLUTION OF THERMAL NETWORK
Electric analogues of the thermal network, ess-
entially special purpose passive-network computers,
have been built. A large number of components
are necessary since all parallel paths must be in
operation at the same time. However, the solution
„ „, 1 ^ , r , ^. ^1. time is short since the time constant of the electri-
Fig . 2 . Thermal network of conduction path
cal path is several decades below the equivalent thermal path. Generally, the machines lack versatility
since the set-up time is long and inevitably special components are needed for most new applications.
Digital computer solution of the thermal network is a sequential process which, at each succeeding
time, calculates for each node in turn a new node temperature that results from the heat flows in the paths
connected to the node in the preceding time step. Thus a temperature history of each node is obtained.
There are two types of node - those with capacity and those without.
a. Nodes with Thermal Capacity.
In the general case, node i will be connected by resistances R^j to a number of surrounding nodes
jj, j2 , etc. The node will have a thermal capacitance C^, a heat input due to mechanisms other than
conduction or equivalent conduction q^ and a temperature Tq at the time 9 .
Quantity of heat entering the node in the interval A© is given by:
Q = q^Ae
'^i
),i
R..
1].
This heat causes a rise in temperature of the node such that
Q = C. (T„ . . „ . - T
Thus,
= C. (T^
+ A 6'i
S ^^e+Ae,i "^e,i^ '"^iA^
e,i
»,i
R. .
1].
whence
n
AS ^^e+Ae,i "^e,i^ " '^i ^
+ A6/i C.
J=l
R. .
1]
n ;
fi, R^. -^6,1 fi, R^.
+ T.
b. Nodes without Thermal Capacity.
(vi)
These will frequently be surface nodes. The heat that enters the node must leave under the action of
the temperature potential of the node.
T - T
e+Ae,i e,j.
T - T
e + AQ-i Q.h
q.Ae =
Ae +
AS +
161
a =T E - £
n
j=l R. .
i=i ^
To ensure stability of the calculation, i.e. to ensure that the finite difference solution is converg-
ent, the time increment A 9 must be less than the minimum time constant for the circuit, i.e.
C,
Ae < (RC) = — ^7 . . . (viii)
£ Rij
J=l
Heat flows can be found from the heat flow in appropriate resistance paths for each time step.
When the heat leaving a conduction path is needed, it can be found from the heat flowing in the con-
ductive resistance connected to a boundary node. For the heat entering the room air, the convective
resistance can be used.
For any given time interval, m A 9 - the average rate of heat transfer towards the node i will be
given by:
™ ^i.m A9 " ^i.m AB
R
m=l ij ,. .
q - ' . . . (ix)
m
The computation of new temperatures by the node equations is simple and requires very short com-
puting time but it must be repeated for each node at each time increment. Since with practical build-
ing systems, large networks of several hundred nodes may be involved and the allowable real time in-
crement is small, maybe of order several seconds, the computing time for a run of several days is
necessarily long, and several days must be run for each case since the error resulting from the ass-
umption of initial temperatures takes two to three days to become negligible.
4. THE COMPUTER PROGRAMME
Though this programme is described as a general purpose thermal network analyser, it has been writt-
en with the aim of allowing easy modification for the addition of special functions. Thus it consists of a
simple main programme as shown on the flow chart (Fig. 3) with many of the operations representing sub-
routines which are on call.
The input data for the programme is as follows:
Resistances - Identification by resistance number; nodes to which resistance connected;
dimensions of resistance element; thermal conductivity.
Capacitances - Identification by node number; dimensions of capacitance element; specific
thermal capacity.
Solar Factors - Latitude. Time of year. Node number; inclination and azimuth; area;insol-
ation on a horizontal surface for each hour.
Cathode follower - Pairs of nodes i and j . (Temperature of node i will be replaced with
temperature of node j).
Radiative resistance - Resistance number; value of e ^-^2'
Convective resistance - Resistance number; area A; exponent m or n for free or forced convection
(Fig. 3).
Table Association - Table number and associated node or resistance number.
Problem constants - Print interval. Problem cut off time . Initial time. Number of tables , etc.
Heat flow calculations - Node number at which heat flow required; resistance number.
Temperature output - Node numbers at which temperature data required,
requirements
Tables - For each table: Table number; argument type; variable type; argument list;
corresponding variable list. (Possible arguments: time, temperature.
Possible variables: temperature, resistance, capacitance, heat input).
The output consists of the temperature of specified nodes at required intervals of time together with
the rate of heat flow, during the previous interval, through separately specified nodes, e.g. the hourly
temperatures of any desired nodes with the heat flows for a separate list of nodes can be obtained.
162
5. TYPICAL PROBLEM
Q
Calculations were made on a simple enclosure (Fig. 4) of fixed internal dimensions. The wall temp-
eratures and total heat flow into the enclosure were determined for wall thicknesses in the range 1-6 inch.
Properties of the two construction materials used, viz. concrete and polystyrene foam, are given (Table I)
as are the heat transfer coefficients and surface absorptance (Table 11).
Table I Thermal Properties of Construction Materials
r UJ. ybLylcIlt: iUalll
-3
Density, lb ft -1-1-1
Thermal conductivity, Btu h ft F
Specific Heat, Btu lb~-^F"-^
140
1.0
4
0.02 2
0.21
0.27
Volumetric heat capacijiy, ^tu ft~~^
Thermal diffusivity, ft h 1-2-1
Overall heat transfer coefficient , Btu h ft F
29.4
1.08
0.
0.02 04
(3" thick, vertical wall)
4.0
0.088
Table II Heat Transfer Coefficients and Radiation Absorptance
Heat transfer
Vertical wall
Inside
2.18
coefficient ,
Btu h~^ft"2F~-^
Outside J
4.0
Horizontal wall
Inside
Outside
2 .44
4.0
Absorptance
Inside
Outside
1.0
0.8
As this work was part of a study of air conditioned buildings for tropical Australia, ambient condit-
ions were chosen to be representative of a typical location. The data (Table III) is for an average sunny
December day in Cloncurry, Australia, an inland town at approximately 2 0°S latitude.
Table III
Time of day, h
Ambient Temp, F^ ^
Insolation, Btu h ft
0
81.5
1
78.6
2
76. 7
3
76. 1
4
76. 1
5
76.8
6
78.5
32
7
88.6
93
8
83.2
167
9
85.8
230
10
89.3
276
11
93.0
3 05
Time of day, h
Ambient Temp, F
Insolation, Btu h"-'-ft~^
12
97.4
315
13
100.0
300
14
100.0
2 64
15
98.2
2 08
16
97.2
141
17
96.5
72
18
96.0
25
19
93.5
20
90.2
21
87.7
22
85.6
23
83.3
24
81.5
The thermal network (Fig. 5) consists of six circuits in parallel representing the paths through the
walls, roof and floor. These circuits are connected to a common node through a resistance network which
models the internal convective transfer. This common node, held at a constant temperature of 78°F,
stands for the indoor air. Other resistances connect the indoor surface nodes to allow for radiative
transfer .
Outdoor surface nodes receive heat flows (Fig. 6) that have been calculated from the Insolation and
are connected through convective resistances to nodes which receive an input of the ambient temperature.
(It will be noted that long-wave radiation from the outdoor nodes is neglected for simplicity).
The floor circuit is connected to a node held at 74°F and representing the constant earth temperature.
The output from the analyses is the hourly temperature of each surface node, the hourly heat trans-
fer rates from each inside wall to the inside air node and the daily heat transfer rate for each wall.
A typical result giving the diurnal heat flow per square foot is shown (Fig. 7). It will be seen that
the roof gives by far the highest rate and that the West wall is next. The North wall has no direct sun-
shine but is affected by diffuse radiation. The South wall shows an effect due to the direct component of
radiation when compared to the North.
Integration of the heat flows on a daily basis was performed for each case (Table IV). For each wall
thickness, the heat flow through each wall was expressed as a fraction of the roof flow, called the re-
lative heat flow. It will be noticed that, even though the roof flow ranges from 36 to Btu day~-^ft~^,
the relative flows for each orientation do not vary significantly.
When wall flows are expressed as a percentage of the total daily flow (Table V), it will be noticed
again that the proportion through each orientation does not depend significantly on the thickness or the
insulation of the wall. (There is a significant increase in the effect of the floor for the well insulated
cases. Polystyrene 4 inch and 6 inch, but the total flows involved at this level of insulation are relatively
small.) •
Total heat flows per day, appearing in this table (Table V), have been plotted against the overall
163
heat transfer coefficient U (Fig. 8). The result is an almost linear increase in heat transfer with increase
in the coefficient, as might be expected.
Table IV
Heat Flow per day per square foot for each orientation
Material
Th if-V -
Heat Flow -
Btu day ^ft ^
Relative Heat Flow
ness
-inch
N
S
E
W
R
F
N
S
E
W
R
F
CD
1
370
540
670
620
100
.34
.50
.62
.57
1.0
09
+->
0)
2
340
490
590
550
990
89
.34
.50
.62
.56
1.0
09
u
c
3
320
460
550
510
910
78
.35
.51
.61
.56
1 . 0
09
o
O
4
300
430
510
480
850
69
.35
.51
.60
.56
1.0
08
c
0
270
380
460
430
750
55
.36
.51
.61
.57
1.0
07
1
67
93
114
107
173
-3
.39
.54
.66
.62
1.0
-0
02
oly-
ene
2
37
51
62
59
95
-12
.39
.54
.65
.62
1.0
-0
12
3
25
35
43
41
66
-17
.38
.53
.65
.62
1.0
-0
26
4
19
27
33
31
51
-2 0
.37
.53
.65
.61
1.0
-0
39
U2
6
13
18
23
22
36
-23
.36
.50
.64
.61
1.0
-0
64
From the network analysis, wall temperatures are also available. The maximum daily temperature
and the time of occurrence have been tabulated for each orientation and two thicknesses of each material
(Table VI). The advantage of insulation is obvious as the temperature is reduced as much as 42°F when
comparing roofs of the same thickness but different material. A further point is the significantly higher
temperatures of the roof, west and east walls when compared with the north and south walls.
Table V
Wall Heat Flows as a percentage of Total Flow
1
in
1
Materia]
Thicknei
inch
N
S
E
W
R
F
Total Fk
Btu day"
10"3
%
%
3
CQ
Crete
1
12 .3
17.
6
16.
1
15.0
35.6
3.
3
125
100
1.26
2
12 .4
17.
7
16.
2
15. 1
35.5
3.
2
114
91
1.14
3
12.5
17.
8
16.
2
15.2
35.4
3.
0
105
84
1.07
c
o
4
12.5
17.
8
16.
2
15.2
35.4
2.
9-
99
79
.96
O
6
12 .6
17.
8
16.
3
15.3
35.5
2.
6
87
70
.83
1
13 .7
18.
9
16.
9
15.9
35.1
-0.
6
20.3
100
16
.22
2
14.2
19.
7
17.
7
16.6
36.6
-4.
8
10.7
49
9
.12
3
14.8
20.
5
18.
5
17.4
38.5
-9.
6
7.1
35
6
.08
4
15.5
21.
5
19.
5
18.3
40.8
-15.
6
5.2
26
4
.06
cn
6
17.2
24.
1
22.
0
20.7
46.6
-30.
0
3.2
16
3
.04
Table VI
Maximum Internal Surface Temperature
Material
Concrete
Polystyrene
Thickness
1
inch
4 inch
1
inch
4 inch
Time
Temp
Time
Temp
Time
Temp
Time
Temp
North
14
93.7
16
89.3
14
80.8
15
78.8
South
17
97.5
18
93. 1
14
81.4
17
79.0
East
8
110.0
10
98.9
8
83.3
9
79.5
West
16
113.7
18
103.4
16
84.0
17
79.7
Roof
13
128.3
14
113.9
13
86.0
14
80.4
Floor
15
81.5
17
80.3
14
78.2
16
77.7
This data was si^bsequently used in an economic analysis of the cost of air conditioning buildings
of ft^ floor area. Cost data for Australian conditions was estimated as follows:
Capital cost of building For U = 0.3 Cost = $7.8ft~^
U = 0.2 Cost = $ 8.6 ft "2
U = 0. 1 Cost = $10.8 ft"2
U = 0.05 Cost = $13.4 ft"2
164
Owning cost of building = 8% per annum
Capital cost of air conditioner = 94 0 t "^'2 8$ ton"-^ (t - refrigerator capacity in
Owning cost of air conditioner = 10% per annum tons)
Operating cost of air conditioner = 22 0 t "'^•'^^$ ton
The average cost levels thus obtained are designated levels A2 and B2 (Fig. 9). Levels and are
approximately ±25% A, while levels B^^ and are approximately ± 45% 82- Thus the range of likely costs
is spanned. The results show that the minimum cost occurs for values of U between 0.1 and 0.2.
6. ALIGNMENT OF THE MODELS
Some experimental work and computation has been performed with the aim of proving the models.
Factors that have been investigated include:
a. One dimensional approach.
It is obvious from the different temperatures that can occur in adjacent areas, e.g. the roof and north
wall, that considerable heat will be transferred in directions other than normal to the wall surface. Thus
the assumption of one dimensional flow must be evaluated. Other factors that can modify the approximat-
ion to one dimensional flow are discontinuities in the structure, such as with stud and panel wall construc-
tion, and the geometrical effect of corners. The effect is dependent, among other things, on the size of
the building and is greater in scale models of buildings especially where the material thickness is not
scaled. Errors greater than 5% can result.
b. Fineness of the mesh.
Studies with electric analogues have indicated that dividing homogeneous conduction paths into four
to five lumps gives sufficiently accurate results. Our studies, using material properties as in Table Land
sinusoidal inputs for which the theoretical solutions can be obtained, indicate that using even three lumps
will enable calculation of heat flow within 5%. There may be greater inaccuracy in the amplitude ratio
which varied up to -7% for the network with three lumps.
c. Heat Transfer Coefficients.
The outside heat transfer coefficient is usually considered as a function of the wind velocity which
varies with height and time. If wind velocity is taken as V^^ f or the surface, it will have different effects
on surfaces of different orientation.
The value of the coefficient has been adjusted within limits when attempting to align calculated and
measured results.
d. Size of the time step.
Since the time step can be of any value less than the stability limit, some results were taken to deter-
mine the improvement in accuracy for time steps as small as 0. 1 of the stability limit. It was shown that
for the system considered, reducing the step to 0.125 of the stability limit improved the accuracy of amp-
litude ratio by a factor of 4. Practically, this would also increase the computing time by almost eight
times and make such small steps uneconomic.
e. Damping of initial value transient.
Initial values of node temperature are usually assumed at some constant value though in practice some
distribution of temperature resulting from the previous variable input will remain. The transient from this
incorrect assumption takes several cycles to become ineffective. The error in the amplitude ratio is reduc-
ed by 44% between the first and second cycle and by only 8% between the second and third cycles when it
is approaching the long term value. Thus it would seem that only two to three cycles need be calculated
to remove this error.
f. Comparison with the van Gorcum matrix method.
The van Gorcum method was compared with the network analyser for some simple problems. Being a
superposition method, it must be used with constant values of the resistances but, for most building pro-
blems, separate averaging of these resistance values will usually give adequate accuracy. The calculat-
ion method does not suffer inaccuracy due to lumping since the distributed properties are used.
Since Fourier components of the input are required, it is somewhat less easy to deal with actual
weather data input over a long period.
7. CONCLUSIONS
A basic inaccuracy arises from the many approximations in modelling a real situation and this applies
to the mathematical model used to calculate the heat flows in a structure. Thus absolute accuracy in the
calculation method is not of paramount importance as long as the calculation error does not unduly in-
crease the overall expected error.
The thermal response methods accurately model the conduction path of one dimensional systems and
can produce heat flows for periodic boundary conditions with a short computing time. Since superposition
is involved, variable convection coefficients and material non-linearities cannot be accommodated. Per-
haps, pulse methods are more flexible in their handling of boundary conditions than Fourier methods.
Lumped parameter networks, analysed by solution of node heat balance equations at finite time steps,
are simple in concept. They are not restricted to one dimensional flow, can handle variable resistances
165
and internal radiative exchange. But, since sequential solution for each node is required at each time
step, the computing time is long. While they can approximate space-wise variations as accurately as
desired by .decreasing thq spatial increments, computing time is increased as the space increment is
decreased.
It would seem that the thermal response method may be more suitable for routine investigations with
programmes adapted for a particular class of work, e.g. routine calculation of heat flow into air condit-
ioned buildings.
On the other hand, the thermal network analyser is suitable for investigational work on a wide var-
iety of problems. It is particularly useful for University type research due to its conceptual simplicity,
its adaptation to parametric studies and its ability to model complex situations.
A
C
F
H
q
Q
R
area, ft _^
thermal capacity, Btu ft
shape factor
insolation on a horizontal surface,
Btu h ft"2
-1
heat transfer, Btu h
heat quantity, Btu _^
thermal resistance, h F Btu
orientation factor, surface to sun
SYMBOLS
t
T
W
a
6e
e
e
p
a
SUBSCRIPTS
temperature, F
temperature, R -1-2
flux density, Btu h ft
absorptance
time increment, h
emittance
time , h
reflectance
Stefan-Boltzmann constant, 0.173 x 10
Btu h" ft"
-2
convective
sol -air
i - any node
i - other node connected to i
REFERENCES
surroundings
at particular time
with time increment
Sheridan, N.R. and Carr, W.H. () A solar air conditioned house in Brisbane, Solar Research
Notes No. 2, University of Queensland, Brisbane.
Mackey, CO. (). Sol-air temperature - a new concept, Heating and Ventilating, Vol. 41,
No. 12, p. 62.
Muncey, R.W. (). The calculation of temperatures inside buildings having variable external
conditions. Aust. J.Appl.Sci. 4, 189-96.
Brisken, W.R. and Reque, S.G. (). Heat load calculations by thermal response, ASHRAE
Trans. , Vol.62, p. 391.
Stephenson, D.G. and Mitalas , G.P. (). Cooling load calculations by thermal response
factor method , ASHRAE Trans . , Vol. 73, Part 1, p. Ill 1.1.
Paschis, V. and Heisler, M.P. (). The accuracy of m easurements in lumped R-C cable circuits
as used in the study of transient heat flow. Trans. Amer. Ins tit. Elec. Eng. , Vol.63, p. 165.
Buchberg, H. (). Electric analogue prediction of the thermal behaviour of an inhabitable
enclosure, ASHI^E Trans., Vol.61, p. 339.
Sheridan, N.R. (). Energy conservation applied to the rational design of a dwelling for the
tropics. Proceedings VlAorld Power Conference, Paper 54, Section IVB.
Sheridan, N.R. (). On solar operation of absorption air conditioners , Ph.D. thesis. Univer-
sity of Queensland, Brisbane, (unpublished).
166
Calculate Tg 4. ^ q
Eqn . (vi)
Read input data
I
Calculate fixed
resistances
Calculate
capacitances
Calculate
solar input
n^u
Interpolate in Tables
I
Calculate radiation
rpsi.qtancpq
q = (1 - p) R AH
iinear interpolation
1
(i)
R =
2.^2
r eF _A (T + Tj(T + T ^ ) (")
s2 s 2 s 2
Calculate convective
resistances
R =
1
Calculate
Z-k.T. T/R.A e
c BA ^T'
ir
°^ R =^
c CA V
C.
tQ < (RC) = — ^
J "^ij
- . . . (viii)
. . . (iv)
Cathode
Follower
I
T = T
e -^9 + A e
No
FIG. 3
PROGRAMME FLOW
CHART
(Counters, etc. are not shown)
167
ground
FIG. 4 VIEW OF SIMPLE ENCLOSURE
168
0 4 8 12 16 20 24
Time - h (from midnight)
FIG. 7 HEAT FLOW IN BUILDING WALLS
169
1.5
/
/
/
X
/
/
X
/
/
X
/
/
/
/
/
/
/
/
X
0 0.5 1.0 1.5
_ 1 _T - 1
Overall heat transfer coefficient 'U - Btu h ft F
FIG. 8 TOTAL HEAT FLOW IN STRUCTURE
lOOOl ' i ^ 1
0.4 0.3 0.2 0.1 0
-1 -2 -1
Overall heat transfer coefficient 'U' - Btu h ft F
FIG. 9 OPTIMUM INSULATION THICKNESS
170
A Method of Computer Simulation
through Modified Signal Plow Graphs and Operator Concepts
and Its Application to Synthesis of Heating-Equipment Capacities
Shigeru Matsuura
Faculty of Engineering
Hokkaido University
Sapporo, Japan
In order to facilitate simulation of a physical system,
direct simulation on an analog computer through a signal flow
graph obtained directly from a schematic diagram in the physical
system Is used in this__ paper. Physical meanings of the method
are confirmed and modified in view of algorithm as follows: (1)
By creating a summing point which defines a signal, a wrong
signal flow graph resulting from two definitions of a signal is
avoided and an Inversion law and interconnection of subgraphs are
clarified. (2) A scaling method in s-domain Is studied only by
the use of a translation of a modified signal flow graph; It is
made possible to obtain the completed program on an analog
computer in which mutual relations between a signal and a scaled
signal (a machine variable) are elucidated. (3) An operator
concept Is developed into the digital domain and a physical
meaning In a closed loop is confirmed, so that simulation on
digital computers by same methods as in the above-mentioned
simulation on analog computers is made possible.
As an application, a synthesis of heating-equipment capacities is
performed together with the confirmation of troublesome points in
the actual operation, where not only a building but also automati-
cally controlled heating equipments are simulated.
Key Words: Algorithm, closed loop, definition point, digital
operation, dynamic balance. Initial value, integral operator,
modified signal flow graph, operator concepts, warming up
load, scaling in s-domaln, space series.
1. Introduction
An environmental design related to buildings would be an optimization of the ways
of combination of components (said to be a structure of system) and their values in a
buildings system containing equipments, which adjusts its entire balance under certain
specified conditions. Considering the use of a computer from the point of view of
design, therefore, it is desirable to use It synthetically rather than analytically,
that Is, It is necessary to be able to talk with the computer. As one of the useful
means for it, there exists such simulation as correspondence of components in a system
one-to-one, because a building system becomes large-scaled, complicated, high-priced
and made-to-order , so that experiments of actual systems are impossible. For the sake
of its usefulness, the technique of simulation has been widely used in fields of
electronics, automatic-control, chemical process and so on.
The types of computers used in simulation are analog type, digital type and hybrid
type (which is the combination of previous 2 types). Considering them from the
standpoint of simulation, there, it shows the problems as follows: (1) There are
differences of the models (expressions) as languages and ways of thinking depend on the
kind of computers. (2) Advanced knowledges and techniques are required for simulation.
(3) As the analog computer has the limited usages except for a differential analyzer or
Systems Engineer
171
a simulator, It Is necessary to consider simulation on the digital computer. However,
the large-scaled and high-speed machine is required in Its case.
As a countermeasure for the above mentioned, it Is necessary to consider the next
points: (1) Investigating programming-rules through models in use of the same concept
which Is Independent of the kind of computers. (2) Using symbolism with sufficient
informations in expression of system and its description. (3) A symbolism with
algorithm which leads automatically from description to program. (4) In synthesis, it
is necessary that a program one-to-one corresponds to a system in parts and the
program is newly made by Interconnection and division according to changing of the
structure In system by interconnection and division, and also values 6n the program can
be easily changed. (5) Finding out physical meanings and investigating calculation
rules which calculation accuracy is not less than it was before even if simple proce-
dures are used for the purpose of using a small machine such as a mini computer or a
desk calculator.
This paper deals with a new method of computer simulation with algorithm which
automatically gets to a simulation program through a model from an object system.
2. Method of Computer Simulation
It is well known that phenomena of system should be expressed in use of elements
and a pair of across variable and through variable with time. For instance, heat
conduction phenomena can be expressed as simultaneous differential equations using
thermal resistance and thermal capacity as elements, and using temperature and heat
flow as across variable and through variable with time. In these equations, relations
among components such as wall and boiler which actually construct the system, namely,
system structure is not clear.
There are graphical symbolisms as a way of expressing this structure, namely a
physical network model, a block diagram, a signal flow graph, an analog computer
diagram and so on. These are diagrammed to emphasize different aspects respectively.
It is performed to symbolize many informations as to relations of actual components
and each element. However, Informations for the casual relation in each variable are
not diagrammed. The signal flow graph and the block diagram are expressed in regard
to the casual relation, but the relation to the actual object becomes weak rather than
the physical network model. In the above expressions, direct Informations of time are
lost. The analog computer diagram has a nature of emphasizing element Itself, its own
function in Itself and connection with other elements.
Observing these expressions from a view of simulation programming on the computer,
with respect to the analog diagram, simulation programming seems to have been
accomplished at one sight. However, as the analog computer diagram is usually
introduced in terms of an expression of slmulataneous differential equations, the
system structure is lost and the correspondence of system one-to-one in parts can not
be found. Simulation In use of this procedure requires to supplement informations
through thoughts of the structure. Therefore, it is very useful to obtain a simulation
diagram by making the best use of the characteristics of each graphical symbolism. 2
That is; at first, the physical network model is Introduced by a schematic graph [ 1]
which indicates actual system; and then, it is transformed into the signal flow graph
C 2] or the block diagram; and finally, the simulation diagram is obtained. However,
it is not always said to accomplish algorithm of final processes. Symbolism
applicable to both computers is, therefore, developed under considerations of terms
of physical concepts as follows:
2.1. Concepts of Signal and Operator
Observing the relations between variables and elements from a new standpoint,
variables are signals which transmit in a system and the signal is modified by the
element, so that it becomes the next signal in succession. Elements should be thought
as operators. Under such thoughts, what is diagrammed in s-domain Is a signal flow
graph. However, it should be noted that descriptions corresponding to a system have
many equivalent signal flow graphs, but physical meaning of the graph is clear only
when the graph is described in the form of 1/s concerning time, namely. In the form of
an Integral operator, because physical phenomena may be said in general to depend on
the past and the conservation of energy principle.
2
Figures in brackets Indicate the literature references at the end of this
paper .
172
2.2. Modification of a Signal Flow Graph
As a simple example to clarify the above mentioned, it is considered that water
is discharged from water tank (across sectional area A) using a pipe (resistance R) .
This is applied also to the case in which heat is discharged only by ventilation out
of the room. When the water level is h, its initial value is hj and outgoing water
flow is q, the modified signal flow graph expression of this system is given as eq (1).
where, the signal flow graph is modified as follows: The signals are enclosed by a
large circle to be distinguished from transmittance (operator) and the new summing
points shown by small circles are made, they are also definition points in signals.
Observing the definition as to h, it is equivalent to the next equation.
h = + -ill
sA g
By the modifications, the next merits may occur. By means of separating and
symbolyzing definition points in such a way as each a signal has only one definition
point (by elimination of signals on the way, it is not prevented that the signal has
sequentially two more definition points), misses in two definitions of a signal, when
the flow graph is drew, can be prevented. Physical meaning of interconnections in
system is in a concordance with across variables and a continuity of through variables.
An interconnection in sub-graphs (which correspond to sub-system) attending an
interconnection of sub-system requires that In any Interconnection the across variables
are connected by a branch with transmittance 1 and the through variable is defined by
another through variables, connected by each branch so that continuity conditions may
be held. In this case, if a signal has two definition points through the interconnect-
ion, here, a branch of either definition point is inversed (in which 1/S is left as it
is) as a definition point for a different signal, and two definitions resulting newly
from it is Inversed in succession until reaches a signal having no a definition point.
Furthermore, by creating this summing point, the analog computer diagram can be easily
expressed by modified signal flow graphs. Namely, a potentiometer, a summing amplifier
and a summing integrator are expressed as eqs (3), i^) and (5). By using them, an
analog simulation diagram corresponding to a system one-to-one can be made only by
equivalent transformations of the graph.
173
(5)
However, if a scaling change Is not done In the analog computer programming, it
is not that the program Is perfect. A perfect analog simulation in only a signal flow
graph is not always done. It means that there remains problems of algorithm. Next,
a scaling in s-domain is considered.
2.3. Scaling in S-domain
A scaling has two kinds, first is to transform variables in a system into machine
variables which are non-dimension and smaller than 1. Transforming them in s-domain
by considering a magnitude scale factor a with dimensions, it becomes as follows:
ax
(6)
For the purpose of representing this relation on a graph it is necessary to add a new
rule, that is, by multiplying a signal by a , the procedure in such a way that a
transmittance of incoming branch is multiplied by a and that of outgoing branch is
multiplied by 1/a is required so that the graph is equivalent to the original graph.
is equal to
(7)
(8)
Next, it is thought to transform concerning time in use of time scale factor
simulation within time or frequency adapted to the machine.
e for
At first, in t-domain
3t
(9)
transforming (4) into s-domain
(10)
where t, s correspond to real time and t
Mixnsky's expression [ 3]
S to machine time. And according to
174
1
(11)
t =
(12)
Observing both sides of these equations from the point of view of a dimension, they do
not coincide because 1/s is said to have a dimension of t.
The next po
result of operat
s-domain, operat
Therefore, this
impulse is though
be affixed to th
the dimension,
the signal is wr
Considering phys
by 6 in time. A
machine time is
ints are considered to clarify this problem. Observing a signal as the
ors acting on a unit Impulse, in a usual description of function in
ors alone are expressed and the unit Impulse is not expressed,
unit impulse having value 1 and the dimension 1/t (because the unit
ht as a limit of a pulse in the width At and the height 1/At) should
e right hand of eqs (11) and (12) and both equations coincide also in
Hereafter, to distinguish clearly a signal from a group of operator,
itten in the form of affixing I having a dimension of 1/t.
ical meaning of time scale change in eq (9), the phenomena is extended
s an area of a unit impulse must be always 1, the unit impulse 1 in
given as :
(13)
A unit step function which results in one integral operator acting on the unit impulse
is expressed as, 1/s, 1/S, respectively. As this unit step function is an Infinite
step without concerning time scale change, they must be equal. And show them as 1/s.
1
S 1
(14)
accordingly
1
6S
(15)
From the above investigation, if time scale change is done directly in s-domain, it
will be done by affixing 1 to input signal and also by adapting eqs (iH) and (15).
For the purpose of showing a simple example of analog simulation procedures, the
graph of the tank model shown already in eq (1) Is transformed equlvalently in such a
way as constructed by analog computer elements given In eqs (3), (4) and (5). And when
magnitude and time scale change are done with regard to the above mentioned, the analog
simulation program can be accomplished automatically and successively as follows:
■<
1
Ch
V
1 A
— o
6a,
(16)
1_
aq
>-
175
where, the values of H and Q are non-dimension and machine variables smaller than 1
and 1/R • /ahj 1/A 'Oih/Sciq are non-dimension and values smaller than 1 and indicate
potentiometer values'.' The newly added branches shown as dotted line indicate relations
between machine variables and variables of the original system (these do not become
the object of the simulation). Next, consider the case of digital operation.
2.4. Digital Operation
In the case of an operation on a digital computer, various numerical methods have
been developed in regard to information which can be obtained when it is sampled. That
is, information related to the structure is weak, so that they don't always adapt to
system simulation. For the purpose, the "time series" method [ 4] and the "thermal
response factor" method [ 5] were published. But it is difficult to adapt the methods
to the next cases; namely (l) when systems are Interconnected, (2) when the system- has
non-linearity, (3) when the system has the initial value which represents the past
effect, (4) when the problem having non-periodic intermitting heating including off
days is solved.
A digital operation of an integral operator is considered, observing that time is
represented only by the integral operator 1/S in the simulation diagram corresponding
to a system one-to-one. When values of a signal at t=0, T, 2T, etc. (T is time
interval) are xg, X]_, x-^j , etc., the signal x is approximated by straight
line segments at each interval. It is expressed as eq (17), which is named "space
series".
[ (Xo) , (Xj) , (x^) , (Xj) ,
(17)
The signal resulting from the integral in eq (17) is expressed by space series as
follows :
I [(0) , (x, + xj
(x,+ X, + X, +
Xo )
(x,+ x,+ x,+
(18)
Therefore, it is proper to replace all 1/s of the graph with the above equation and
calculate it step by step at each interval. However, as exceptions, when the signal
value is always zero in the previous interval and it rises to the value (xq), an
operation of 0 + (xq) = (0) must be used, and in a unit impulse, the calculation is
such that instantaneously (1) will be preserved.
Next, consider adaptation of the digital operation in eq (1). When eq (1) is
solved theoretically with Mason's rule [ 6], eq (20) is given as:
ST.
1 + STr
(20)
176
where, = AR Is time constant. Equation (1) Is expressed in the form of the digital
operator using sampling interval T as follows:
177
Table 1. Comparison between calculation values in use
of y= T/Tc = 0.25 and theoretical values.
Time
Time (by T^)
Calculation
Value
Theoretical
Value
0
0
1
.
1
T
0
25Tc
0
.
0
2T
0
5 Tc
0
. 6o49
0
C r\ C r-
3T
0
75Tc
0
.
0
4t
1
0 Tc
0
.
0
5T
1
25Tc
0
.
0
6T
1
5 Tc
0
.
0
7T
1
75Tc
0
.
0
8t
2
0 Tc
0
.
0
12T
3
0 Tc
0
.
0
i6t
4
0
0
.
0
When M = 2 (namely the interval of 2 Tc), eqs (22) and (23) become zero (these
exact values are 0. and O.OI). And when y> 2, they oscillate in +, -, +,
, etc., having values smaller than 1. Therefore, it is seen that y is an index
for modelizing a distributed system into a lumped system. That is, time constants in
each part should be divided to coincide as much as possible. In order to clarify
correspondence to the system, if divisions are done in such a way that time constants
in each part have considerable differences , the interval in calculation of each part
should be modified in such a way that y becomes equal in parts. For the purpose of
rough calculations, when the calculations are tried with large intervals, it is proper
to neglect heat capacities in the part of y> 2.
3. The Application to Synthesis of
Heating Equipment Capacitance
In use of the methodology mentioned above, it is reported to simulate hot water
heating in a building on an analog computer. A one-story house (100 m^ ) having
concrete walls of thickness of 15 cm affixed with glasswool 5 cm is heated by hot-water
radiator and the system is represented in figure 1 using physical network model. As
the used computer is small, the building is one-room model with one boiler (with hot-
water-supply tank inside) having one radiator, and a burner is controlled ON-OFF by
room temperature and water temperature in the boiler.
3.1. Warming up load
As the results of simulation, figure 2 Indicates an intermittent operation in
which an operation is sixteen hours and a stoppage is eight hours. In this case, an
average outside air temperature is -10°C and a calculation load in steady state is
kcal hr~l.
Observing the results, at night the room temperature in stoppage of operation
falls from 20°C to 6°C, therefore, it seems as if fuel is saved in general. But judging
from figure 2, it is said that the sum of outgoing heat flow falls only a little. The
reason is that heat stored in the wall is discharged at night and the heat is
coijipensated during warming up time. It requires about three hours until it reaches
20 C even when a burner of kcal hr (two times of calculation load) is used.
In this example, the intermittent operation has not saved even 10 compared to the
continuous operation and it is clear that the burner output from 2 to 4 times larger
than the steady state load, would be required, corresponding to the interval of
warming up time. Therefore, considering initial cost, the continuous operation is
profitable rather than the intermittent operation.
3.2. The Need of Dynamic Balance of System
Figure 3 indicates ON-OFF of the burner and the boiler water temperature, there.
178
the ratio k of the radiator capacity in steady state to the burner capacity is changed
to 1.0, 1.1, 1.2.
As the result, in spite of having no troubles in steady state, it is seen that
in transient state of warming up time, the boiler water temperature reaches a limit
and the ON-OFP operation begins before the room temperature reaches 20'^C. This ON-OPP
operation means that the burner output becomes smaller. Therefore, it is necessary to
consider not only static balance of system in steady state but also balance in
transient state.
3.3. The Drop in Hot Water Supply Temperature
and Additional Load in Hot Water Supply
Figure 4 Indicates the drop of the hot water supply temperature and an influence
on the room temperature when the hot water is supplied in thirty minutes at the rate
of 10 SL every minute. At that time, there are two cases such as the Intermittent
operation with the burner output in kcal hr"-'- and the continuous operation in
kcal hr~l.
From the results of these simulations, it Is seen that when limit design of
equipment capacities and so on is done, each simulation should be done case by case
because the characteristics are different because of the differences of the systems
and therefore limit design should be determined after confirmation and investigation
of problems.
4. Other Considerations
By means of the concept of the operator (the concept of the very system element
Itself which is the operator) and the modified signal flow graph (where it indicates
that signals are modified by the operators), algorithm was reported where simulation
will take place from the environmental system related to building to its simulation
automatically and continuously without regard to the type of computer. It will be
thought that the description method is also convenient for common expressions of
phenomena in fields of environmental engineering such as electricity, electronics,
dynamics, fluid dynamics, process and so on.
As the example of synthesis only the methodology using the small analog computer
was indicated . If a large-scaled analog computer is used, it is possible to indicate
each room. As digital computers occupy the major parts in general, simulation in use
of the digital computer should be indicated. Languages oriented conversations with
computers are in the stage of development in our laboratory. It will be discussed on
another occasion.
5. References
[ 1] Samuel J. Mason and Henry J.
Zlmmermann, Electronic circuits,
signals, and systems, John Wiley &
Sons, Inc. (I96O).
[ 2] Louis P. A. Robichaud, Maurice
Boisvert, and Jean Robert, Signal
flow graphs and applications,
Prentice-Hall, Inc. (I962).
[ 3] Jan Mlkusinskl, Rachunek operatorow,
Panstwowo Wydawnictwo Naukowe,
Warszawa ( ) .
[ 4] A. Tustin, A method of analyzing the
behaviour of linear systems in terms
of time series, Inst. Elec . Engineers,
Vol. Part II-A, No. 1, p. 130-142,
() .
[ 5] D. G. Stephenson and G. P. Mitlas,
Cooling load calculations by thermal
response factor, ASHRAE Transaction,
Vol. 73, Part II, p. 72 ().
[ 6] Richard S. Sanford, Physical networks,
Prentice-Hall, Inc. (I965).
179
Fig 1 Physical Network Model
6: temperature, C: heat capacitance, h: burner output,
q: heat flow, r: resistance
(Subscripts)
a: room, b: boiler, c: cold water, g: glass, h: heat water supply,
i: inside, o: outside, p: room wall, r: radiator, v: ventilation,
w: wall
Fig. 2 Response concerning h, Qqy,, Qy^ and
for Intermittent Operation
M
/.
Fig. 3 Response concerning h and
6^ for Intermittent Operation when
k = 1.0, 1.1 and 1.2
1,
1""
i
A
1-^-
1 '
-■-1
1
1
>
i
i
- 1
1
i
— 1
-r—
i
- j
1
Fig. 'I (a) Response concerning Gj^ and 6^ for Intermittent Operation with
h = kcal hr"^
(b) Response concerning 6^ and Oa for Continuity Operation with
h = kcal hr"-"-
180
Shared Time System Computer Programs for
Heating and Cooling Energy Analysis of
Building Air Conditioning Systems
Charles J. R. McClure and John C. Vorbeck
Mechanical Engineering Data Services, Inc. (Medsi)
Saint Louis, Missouri
Heating and cooling Energy Calculations are made by shared time computer programs using
Weather Data taken from Air Force Manual 88-8 and U. S. Weather Bureau Climates of the States cover-
ing 218 areas in the United States.
Three basic programs are used. Reheat, Heat-Cool-Off, and Multizone or Double-Duct to produce
net requirements of ton-hours and BTU x 10^. In addition to the weather file, 91 numbers are required
to describe building gains and losses, heating and air conditioning system and building use.
The output file of these programs are processed in another program to convert the ton-hours and
BTU X 10^ building requirements to KW, KWH and BTU x 10^ input to equipment by additional data of 32
numbers describing the equipment and efficiencies.
In addition to evaluation of the three basic systems, analysis may be made of the effects of many
variations of each system and programs schedule, such as:
Economiser system with or without reset of mix air temperature.
Hot deck temperatures on cooling cycle.
Perimeter heating loads .
Reduced temperature in unoccupied hours; intermittent operation in unoccupied hours.
Fuel conversion efficiencies; electrical demand.
Modifications and combinations of these basic programs may be used to evaluate Variable-Volume;
Variable Volume with reheat; Fan-coil units in exterior and Multizone in interior; etc. The programs have
also been used to analyze energy requirements of all electric and total energy systems. Mechanical and
electrical systems for schools, office buildings, hospital operating suites, hospital patient rooms,
apartment buildings, shopping centers and even a bicycle shop have been analyzed with the use of
these programs .
This system of calculation by computer is an outgrowth of many years of experience using manual
calculations. Programming, using Basic Language, was started in March and improvements con-
tinue to the present day.
Charles J. R. McClure and Associates, Inc., the developer of the system, has been making
practical use of the information provided for several years. Medsi' s customers have been using the
programs on their own terminals since November .
Approximately 25 seconds of processor time are used with about 30 minutes connect time for each
run; programs are available from a restricted library on SBC,Cal]/360 system.
Keywords; Energy, heating, cooling, air conditioning systems, shared time programs,
evaluation, gas, oil, electric, dollars.
181
1 . Objective
The Engineers associated with developing these programs have made many estimates of heating
and cooling energy requirements for building mechanical systems by manual calculations using degree
days, full load hours, average temperatures, typical 24-hour weather profiles for each month, etc.
The last manual calculation in consumed over 2 ,000 man hours, most of which was spent in deter-
mining the net ton-hours and BTU x 10^ required by the heating and air conditioning system, without
regard to efficiencies of machinery. About this time, a computer time sharing system became available
and management decided to exploit the computer's ability to make many calculations in a very short
time .
The objective was a monthly tabulation of net ton-hours and BTU x 10 , as shown in Table 1,
with high accuracy and requiring a minimum of repetitive manual calculation.
TABLE 1 . - Ton-hours and BTU x 10
SAMPLE! OFFICE BLDS. MINNEAPOLIS DEC 1.
FIN TOBE RADIATION AT EXTERIOR. CONVENTIONAL RETURN
SYSTEM #1 WITH ECONOMISER
MULTIZONE OR DOUBLE-DUCT SYSTEM
MONTH PERIOD TON HOURS BTUX10«5 INT BTUXlOtS EXT
JAN
NIGHT
0.0
476.6
782. 1
JAN
DAY
0.0
739.8
6 39.0
JAN
EVNG
0.0
370.8
751.3
SUB
TOT
0
FEB
NIGHT
0.0
417.3
656. 1
FEB
DAY
35,0
644.9
494.0
FEB
EVNG
0.0
326*6
614.7
SUB
TOT
34
31 53
MAR
NI GHT
0.0
414.5
*
MAR
DAY
249 • 1
671.2
MAR
EVNG
6.3
549 5
SUB
TOT
255
APR
NIGHT
139.1
333.6
402.6
APR
DAY
. S
49 1 . 3
885. 2
APR
EVNQ
343.0
256.7
338.3
SUB
TOT
MAY
NIGHT
832. S
249.6
855.8
HAY
DAY
.9
318.9
100.9
MAY
EVNQ
.2
176.2
198.8
SUB
TOT
JUN
NIGHT
.7
167.4
183.1
JUN
DAY
.3
212.5
89. 1
JUN
EVNG
.9
117.6
66.6
SUB
TOT
736
JUL
NIGHT
.0
138.7
81.0
JUL
DAY
.4
176.9
8.6
JUL
EVNG
.0
99.4
45.5
SUB
TOT
550
AUG
NIGHT
.2
146.9
88. I
AUQ
DAY
1 .8
180.9
10.1
AUG
EVNG
.0
105.3
50.7
SUB
TOT
582
SEP
NIGHT
.2
229.3
807.0
SEP
DAY
.4
263.6
61.5
SEP
EVNG
.9
164.2
169.8
SUB
TOT
OCT
NIGHT
369.7
311.1
342.1
OCT
DAY
.5
4S5.7
144.1
OCT
EVNG
533.0
240.6
301.6
SUB
TOT
NOV
NIGHT
22.2
370.5
528.7
NOV
DAY
592.2
639.0
396.7
NOV
EVNQ
43.0
304.5
500.9
SUB
TOT
657
DEC
NIGHT
0.0
441.0
696.0
DEC
DAY
0.0
727.6
574.8
DEC
EVNQ
6. 1
350.5
665.4
SUB
TOT
6
TOTAL NIGHT
.7
.7
.8
TOTAL DAY
.0
.2
.5
TOTAL EVNQ
.5
.4
. 1
ANNUAL TOTAL
.1
.3
.4
2 . Weather
Previous experience indicated that Air Force Manual 88-8, "Engineering Weather Data" (1),
should be the weather source, since it was available, compact, included 8,750 observations per year,
and covered many areas throughout the world. Weather observations in AFM 88-8 are grouped into 3
182
periods of the day, 1 A.M. to 8 A.M. (night), 9 A.M. to 4 P.M. (day) and 5 P.M. to 12 midnight
(evening). The accumulated monthly observations are also grouped into 5 degree dry bulb segments to-
gether with the mean coincident wet bulb. In addition to the hours of dry bulb and wet bulb there is
stored in the weather-file the hours of sunshine for each period of each month together with solar heat
gain factors for each period as compared to the maximum hour in July for 9 exposures (N, NE, E. . . NW,
Horizontal). Hours of sunshine for each locality are taken from U. S. Weather Bureau's "Climates of
the States" (2) and solar intensity is calculated by computer using the method outlined in "ASHRAE".
Medsi has weather on file for instantaneous call for over 10 locations in the United States. Each
weather file takes 3 or 4 units of storage on Call/360. To prepare a weather-file for another location
costs about $100, During each run the first part of the weather-file is read into a two-dimensional array,
45 by 125 maximum, and the second part covering solar gains is read into ten one-dimensional arrays
of 36 factors each. Review of many projects leads to the conclusion that these weather-files are the
most accurate input of all the data that enters into energy calculations.
3 . Input Data
The input data required is shown on Medsi form No. 1 (Rev. 12-1-69) (Table 2). The data is en-
tered into the program in the form of data statements together with job identification in the form of print
statements. These are best prepared off-line by punch tape and then entered into the system. These
are entered, given a name (program file) and saved. It is then possible to 'WEAVE' this program of data
statements with other programs such as a reheat program, multizone program, heat-cool-off program
etc. , to readily make comparisons.
3 . 1 Occupancy Schedule
Lines 1 through 4 of form No. 1 (Table 2) are the occupied hours expressed as a decimal part of
the total hours of each period. These numbers can be changed for each month so that vacations and
holidays may be considered. The first number of line 1 is .2 08 and tells the computer that 20.8% of the
January night time hours are occupied, that the outdoor CFM () shown on line 16 is to be used, that
the room temperature is 75 degrees as shown on line 5 and that the first number of lines 24 (BTUH light-
ing gain), 26 (BTUH other sensible gain) and 28 (BTUH latent gain) are to be used for these hours.
Medsi form No. 2 (Table 3) is used to determine these numbers. Schedule C, occupancy, is filled in
with X in the occupied hours of the week. The number of x (12) divided by 56 (8 hours per day x 7 days
per week) equals ,215. Multiplying this by 30/31, to allow for 1 holiday in January, gives .208.
3.2 Temperatures, Humidities and Enthalpies
Temperatures, humidities and enthalpies of the air throughout the system are entered on lines 5
through 14, and line 18. The room dry bulb (line 5) is used in both winter and summer calculations dur-
ing occupied hours. To simplify calculations, enthalpies (BTU/# AIR) are used instead of Wet Bulb
Temperatures and specific humidities (Grain s/# AIR) are used instead of relative humidities. Lines 9,
10 and 11 are summer conditions of air in the supply duct of a terminal reheat system or the cold deck
of a multizone or double duct system. Lines 12, 13 and 14 are winter conditions at the same points
when cooling by refrigeration is used in winter.
3 . 3 Air Quantities
The total air quantity circulated is entered on line 15 and should be the actual air quantity circu-
lated. The actual minimum fresh air is entered on line 16, The use of outdoor air for cooling in winter,
instead of using refrigeration, is called an economiser in this set of programs and is considered later.
Line 17 is unoccupied CFM or infiltration and is applicable to all unoccupied hours. However, since
the refrigeration is usually turned off in unoccupied hours, the unoccupied CFM should be typical of
the heating season.
(1) Figures in parenthesis indicate the literature reference at the end of this paper.
183
TABLE 2
Medsi Form No. 1
MEDSI
Form No. Ifflfl/. 12-1-69i
DATA STATEMENTS (91 NUMBERS!
OCCUPANCY
SCHEDULE
Project JAMlPte. '^FlCt 3u»/l.P/A/g.
Location M I t^l^ t. k Pt\ I f^iiJiy Date I^/i/L^
Night
Day
Evng.
Jan.
April
July
77 1
Oct.
,X,f
NiEht
Day
Evng.
Feb.
May
■11
Aug.
.11 r
r.j
Nov.
•'1
Night
Day
Evng.
IMar.
.(fi>
June
.r»»
■nx
Sept.
.i«y
.'71
Dec.
r'l*
DESIGN CONDITIONS:
5
Room Dry Bulb WINTER & SUMMER)
7S
6
Room Enthalpy (SUMMER)
ly.i.
7
Room Minimum Humidity, Grains / lbs.
e
8
Outdoor Enthalpy Max, (SUMMER DES.I
9
Summer Supply Dry Bulb
10
Summer Supply Humidity, Grains / lbs.
.TK'
n
Summer Supply Enthalpy
12
Winter Supply Dry Bulb
13
Winter Supply Humidity, Grains / lbs.
14
Winter Supply Enthalpy
16
Total CFM
16
Outdoor CMM Occupied
3 < 0 »
17
Outdoor CFM Unoccupied
y * » t
18
Summer Mode Hot Deck Temp,
ts
19
Max, Trans, Loss in BTUH
Sit oo
20
Heat Loss Design Temp, Diff,
fS
21
Max Trans, Gain in BTUH
22
Heat Gain Design Temp, Diff,
(ZERO IF NO WINTER HUMIDIFICA TION)
USED WHEN
THERE IS NO
ECONOMISER CYCLE
(NOT LESS THAN ROOM OR Y BULB)
SOLAR GAINS (Maximum in Julyl
SE S SW
Horiz.
tr»co
LIGHTING GAIN
Occupied
Unoccupied
OTHER SENSIBLE GAIN
Night
Night
S/ eta
26
Occupied
Night
27
Unoccupied
Night
0
LATENT GAIN
28
Occupied
Night
29
Unoccupied
Night
•
Day
Day
Day
Day
Day
Day
Evening
Evening
Evening
Evening
Evening
Evening
/7 e eto
i-y too
DECIMAL OF
TRANS. HEAT LOSS
DECIMAL OF
LIGHT HEAT APPLICABLE
EXTERNAL AREA
INTERNAL AREA
RETURN AIR
DECIMAL OF HORIZONTAL SOLAR GAIN TO RETURN AIR
DECIMAL OF TRANSMISSION GAIN TO RETURN AIR
SUPPLY FAN HEAT IN BTUH
RETURN FAN HEAT IN BTUH
to v»e
3.4 Building Gains and Losses
The transmission (conduction) loss is put in line 19 and the temperature difference used in the
calculation is put in line 20. The transmission gain, not including solar gains, and the temperature
difference are entered in lines 21 and 22. Solar gains are placed on line 23. They are not coincident
solar gains but rather, are maximum gains for the peak hour for each exposure. For example, solar
gain for East occurs about 8 A.M. and for West about 4 P.M. but the values would be the same if they
were similar in glass area, shade factor, etc. These gains and losses should not include any safety
factors or pick-up allowance that might be normal considerations for apparatus sizing.
3.5 Internal Gains
Lines 24 through 29 are internal gains applicable in night, day and evening periods when occupied
and when unoccupied. These values (BTU/Hr.) are calculated manually using the schedule charts
shown in Table 3. as follows. The schedules are filled in with percentages of maximum for each hour
for each day of the week. The occupancy schedule C shows 12 x "s representing 12 occupied hours in
the night period. The percentages of lighting for these 12 hours shows 6 hours of 15%, 5 hours of 100%
and 1 hour of 50%. The average occupied night hour has 50.5% of the lights on and if the maximum heat
gain from lights is 340,000 BTU/Hr., the heat gain for each night occupied hour is 172,000 (the first
184
number on line 24 of Figure 2). People gains, sensible and latent are determined in a similar manner.
Miscellaneous gains, if the energy source is electrical energy, such as an air cooled electric refriger-
ator in the space, should be included in with lighting gains since these loads will later be connected
to ?CWH. Otherwise, include appliance and intermittent equipment loads in other sensible and/or latent
gains .
TABLE 3 - Medsi Form No. 2
MEDSI
FORM N-:2.
ENERGY LOADS PROGRAMS:
SCHEDULE A
SCHEDULE B
SCHEDULE C
o
«
Hours
Peopla
As Percent Of Max.
Lights
As Percent Of Max.
Occupancy
Occ." )f , Unocc.= 0
Period 1
S
M
T
w
T
F
s
S
M
T
W
T
F
s
S
M
T
w
T
F
s
1 Night
01
0
0
o
o
0
e
a
.li
.IS
.if
If
Night 1
02
0
*
0
»
o
0
•0
.If
i<
.If
.If
.ir
li*
03
0
0
(9
e
•
o
0
■If
/<■
.11
;«
04
0
0
O
0
•
«
o
//
.(f
■iS
.>{
.if
f
05
e
«
e
0
0
0
■If
»r
.li
.iS
.If
.If
vf
06
«
•
•
o
»
0
jf
jf
ii'
.if
.1%
.if
07
0
0
o
0
0
j%
.If
.if
.if
.if
./>
X
X
X
X
08
e
.y
,¥
■i
.iS
/.
1.
A
>!
/.
.f
X
X
X
X
X
Doy
09
0
/.
/
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Max. People Sensible ^o. o Schedule)
Mox. People Latent i*e . a »0 (a Schedule.)
Max. Lights Sensible ?V«;.*«0 (b Schedule.)
3.6 Division of Building Heat Losses
and Light Heat Gains
Figure 1 represents the floor plan of a building with area 5 being an office with a window and
area 7 being an interior office. It is apparent that the lights in area 7 cannot be expected to aid in the
heating of area 5; neither can the cold glass in area 5 help cool area 7. Consider also, figure 2 which
represents a store with only the window and roof exposed to the weather. The lights in this instance
can be expected to help offset heating load. However, if fin tube radiation is added to offset heat
losses of the glass (Fig. 3) then the light can only be applied to the heat loss of the roof. It is neces-
sary that some consideration be given to this problem and lines 30 through 34 have been provided for
entering percentages of heat losses, and applicable light heat gains. Lines 32, 33 and 34 are
used primarily for ceiling return systems.
185
3.7 Fan Heat
Heat of the supply fan and return fan are entered on lines 35 and 36. The brake horsepower times
should be used unless the motor is in the air stream in which case KW input to the motor times
should be used.
4.0 The System Programs
The programs that process the input data to produce ton-hours and BTU x 10^ are:
*HCE1RH - Reheat System
*HCE2HCO - Heat-Cool-Off System
*HCE3MZ - Multizone or Double Duct System
Basic procedure common to all three programs is illustrated in the logic Diagram, Figure 4. As
indicated in the diagram, each of the 36 time periods that make up the weather year are printed after
the influence of each weather incident is calculated with the input data . The programs determine solar
heat gains, external heat losses and gains, and internal gains and losses, process this raw building
load in the unique features of the selected system program, calculate part load hours and accumulate
the totals of the various out put information.
4.1 Reheat Program
Figure 5. Logic Diagram, Reheat Program (*HCE1RH) illustrates the considerable complexity of
analysis used to reflect the performance of this system in meeting the building loads. When the out-
door temperature is lower than room dry bulb, the program accounts for the effect of economiser cycle.
A determination of the mix air temperature is made, based on input data concerning reset range of mix
air if used, and, if the O.A. temperature is lower than the adjusted mix air temperature then the cooling
effect of the O.A. is calculated. The quantity of reheat is calculated for conditions when the space
needs additional heat and added to the heat required to preheat O.A. and to humidify. This program
allows for 3 degree shift in room temperature before the reheat load is figured to account for thermostat
throttling range. These calculations are done for each different weather condition.
If there is no economiser cycle, the program calculates required reheat for the mix air temperature
resulting from the introduction of the minimum quantity of ventilation air. The refrigeration load re-
quired to cool the supply air down to the design supply temperature is adjusted to reflect the cooling
effect of minimum O.A. If the space does not require the full available cooling effect, then the program
calculates the necessary reheat and determines required heat for humidification . A separate loop is pro-
vided to account for a special control cycle that will use 100% O.A. when the outdoor wet bulb temper-
ature is below return wet bulb.
When the outdoor temperature is above room dry bulb, the program calculates the reheat needed
in the same manner as with the economiser cycle. However, the refrigeration requirement is determined
as the sum of the minimum O.A. sensible cooling, return air heat gain, supply fan heat, space heat
gains and the heat added as reheat plus the latent heat load from internal loads and outdoor air de-
humidification. The same loop as above is available to reflect 100% O.A, when outdoor wet bulb is
below return wet bulb. The program also accounts for the scheduled mode of operation during unoccupied
hours .
4.2 Heat - Cool- Off System
Logic Diagram Heat-Cool-Off (*HCE2HCO), Figure 6, illustrates the calculation procedure for
this system. When the outdoor air is below room dry bulb temperature, and the building internal gains
exceed the heat losses, the program accounts for the cooling, heating and humidification required for
minimum O.A, , and then determines if the system is in occupied mode and if there is an economiser
cycle. The heating needs for humidification and building refrigeration loads are calculated. When
the outdoor temperature is below room temperature and the building internal gains are less than the heat
losses, the program calculates the heat required for treating the minimum fresh air and supplying heat
to offset the losses. When the dry bulb is not lower than room dry bulb, the computer determines the
186
cooling required to offset sensible and latent gains, including minimum O.A. , and then adjusts this
figure to reflect a reduction in latent load proportional to the ratio of total load to the size of the cooling
system. A loop of computer operations will take account of a special control cycle that provides 100%
O.A. when outdoor wet bulb is below return wet bulb. The program also can determine the refrigeration
load in unoccupied cycle if desired.
4.3 Multizone or Double Duct System
Figure 7. Logic Diagram, Multizone or Double Duct System shows the analysis employed to ac-
count for special considerations inherent with this system. Separate modes of calculation are used to
reflect the system performance when the relationship of outdoor air temperature to room temperature
changes as in *HCE1RH and *HCE2HCO. By-pass factor is the percentage of supply air that goes
through the heating coil and this value is determined for each weather condition. The influence of the
economiser cycle on cooling and heating energy use is calculated; heat required for humidification is
determined for each new condition of outdoor air quantity, enthalpy and internal latent gain. The influ-
ence of 100% O.A. when outdoor wet bulb is lower than return wet bulb is calculated. Refrigeration re-
quired is calculated using the adjusted by-pass factors and including the latent heat load of outdoor
air. (The factor .633 is a constant converting grains per pound of air to BTU per CFM) . Use of the
recalculated by-pass factor reflects the changing conditions of face and by-pass control and is valid
when the by-pass is merely untreated mix air, as when no heat is added to a hot deck in the summer
cycle, and when there is heat added to the by-passed air.
5 . Running the Program
As a check on number of entries and to provide a permanent record of the input data used for the
run, it is good practice to weave *HCEDATA program with the data entered. If the number of entries
checks, the Form 1 data will be listed in full. After this check, the data program is then weaved with
the appropriate system program, *HCE1RH, *HCE2HCO or *HCE3MZ. An outfile must be established
to receive the output and, when the "Run" command is given, the program will ask the following series
of questions .
"Enter Input File Name": Response is the name of the desired weather file.
"Enter Output File Name": Response is the name assigned for the output data.
"Do you want hours and part load": If the response is negative, the program by-passes this por-
tion of calculation and some computer time is saved. A posi-
tive reply causes the program to calculate the percentage of
boiler and chiller load required for each weather incident and
to accumulate the number of hours of each part load increment
"What is the tons of refrigeration machine": Respond with actual machine size selected.
"What is the MBH output of boiler": Respond with actual boiler size selected.
"What is the unoccupied winter room temperature setback": Response is the net difference from
occupied room temperature (Form 1, Item 5). There is no
allowance built in for "Spindown" or "Pick-up". It is as-
sumed that adequate controls are provided to prevent estab-
lishing peak demand for heat pick-up by staging ventilation
loads or similar control over load segments .
"Is there economiser cycle": Response indicates whether outdoor air will be used to remove ex-
cess heat gain during the heating cycle. In Heat-Cool-Off
program the amount of outdoor air above the input minimum
ventilation air is determined by room heat gains only. In both
the Reheat and Multizone programs, the quantity of additional
outdoor air is the amount required to m.aintain the input mix
air temperature.
187
"What is the economiser mix temperature at 0° outdoors": Response is to indicate the upper limit
of mix temperature reset if a variable control is used.
"What is the economiser mix temperature at 55° outdoors": Response must be 55° or higher. If
variable mix temperature is used, the program will calculate
the specific temperature for each weather condition, as a
linear function.
"Is CFM all outdoor air on cooling cycle when outdoor wet bulb is below return air wet bulb":
Response should indicate if this control feature is used.
"Is system off in unoccupied hours when outdoor dry bulb is above room dry bulb": Response
should indicate if system is stopped in unoccupied mode
during cooling season.
When the last question is answered, the computer will print out the ton hours and BTU x 10^ as
shown in Table 1 . These values are the net load requirements of the building for the system selected
and operational program used.
6. *HCENERGY Program
The outfile created by the *HCE System program may be used in a supplementary program,
*HCENERGY, along with additional input, to produce the total fuel and electrical energy input required
for the apparatus selected for the project,Table 5. Output of this supplementary program is illustrated
in Table 4 and is arranged to facilitate comparative analysis of several alternatives of equipment
selection and fuel source.
Additional input information describing the characteristics of the apparatus to be used in serving
the building loads must be entered on Medsi Form 3, Table 5. The reduced load performance character-
istics, capacity and quantity of boilers, chillers, towers and pumps is related to the part load hour
calculations made in the HCE System program to account for variable energy conversion efficiency.
Additional data concerning domestic hot water loads other electrical loads that are not considered in
heating-cooling calculations and some further operational schedule data as included in the 32 entries
on Form 3. Methods of loading the data and running the programs are the same as described above.
- 6.1 Part Load Hours
*HCENERGY has another option that will print out the list of hours of part load of the refrigeration
plant and the heating plant as illustrated in Table 6. The information printed shows the number of hours
the plant will operate at, for instance, 50% and 66% of full capacity and may be used to select incre-
ments of plant size in multiple machine installations.
6.2 Dollars
An additional supplement in the Medsi library will read the output of *HCENERGY into a cost of
energy program. This routine is developed to permit use of utility and fuel rate features peculiar to the
project location. The local data must be written into the program by the user, or it can be programmed
by Medsi.
7, Alternatives and Variations
Since one complete run as outlied above uses so little computers time, it is economical to com-
pare other systems and combinations of systems to evaluate alternatives available. One such combina-
ticn, illustrating the flexibility of these programs, might be a multizone system in the interior with fan
188
coil units at the exterior. This is easily run by separating the data into two segments as though each
system were serving a separate building and running the appropriate data with *HCE2HCO and *HCE3MZ.
TABLE 4 - Output of KW, KWH and BTU x 10^
SAMPLEI OFFICE BUILDING. MINNEAPOLIS DEC 1>
FIN TUBE RADIATION AT EXTERIOR. CONVENTIONAL RETURN
SYSTEM *l WITH ECONOHISER
MULTIZONE OR DOUBLE-DUCT SYSTEM
LIGHTING
BOILER
ACC
SUPPLY t
MISCEl^EOUS
( HTS
PIMPS
EXHAUST
FANS
O.ECTRICAL
KV
KWH
KW
KVH
KW
KWH
KW
KWH
OAN
100
0
557
18
10
FEB
100
0
503
18
10
MAR
too
0
557
18
S398
10
APR
100
0
536
18
10
MAY
100
0
538
18
10
JUN
100
0
477
18
10
JUL
100
0
458
18
10
AUG
100
0
469
18
10
SEP
100
0
511
18
10
OCT
100
347E4
0
553
18
10
NOV
100
33S67
0
539
18
10
DEC
100
0
557
18
10
TOT
6e6e
ABSORPTION ELECTRIC TOTAL TOTAL
REFRI6 REFBIG ELECTRIC ABSORPTIOH ELECTRIC
PUMPS.FANS PUNPS,FANS REFRIG REFR18 REFRIfl
« AUX t AUX MACHINE SYSTEM SYSTEM
KW KWH KW KWH KW KWH KW KWH KW KWH
•J*^" 0 0 0 0 0 0 188 188
0 6 0 3 0 34 188 188
7 45 4 88 46 255 136 180
^ 634 4 403 70 136 S 803
^ '> «029 70 136 803
JW 7 4 70 136 803
JUL 7 4 70 136 203
AUG 7 4 70 136 203
SEP 7 4 70 136 803
OCT 7 4 680 70 136 803
"OV 7 119 4 75 46 657 136 180
DEC 0 1 0 0 0 6 188 188
TOT
FUEL
INPUT BTU X
10>6
RESISTANCE KWH AT IOCS
err
HTS
U.W
. A6S0RP.
TOTAL
HEATING TOT HTS «
H.W.
KW
KWH
KWH
JAN
575
8
0
583
862
FEB
492
7
1
501
868
MAR
485
8
9
503
816
APR
355
7
136
500
198
MAY
842
8
345
595
198
JUN
143
7
455
607
126
JUL
109
8
499
616
186
AUG
115
8
509
638
126
SEP
207
7
361
577
140
OCT
317
8
888
553
198
NOV
447
7
85
481
816
DEC
539
8
0
547
862
TOT
96
As the maximum cooling or heating calculated by the programs during any period is not limited to
the cooling capacity of the total CFM, the reheat program may be used to evaluate an induction system
by letting the total CFM be equal to the primary air CFM and using the proper temperature, outdoor
CFM etc.
Medsi's library contains program variations for evaluating:
Variable Volume systems
Variable Volume with reheat
Internal Source Heat Pump
These programs have been used as a base for evaluating simultaneous energy requirement for
Total Energy Plants and heat with light systems, and recently, one user is estimating the air pollution
caused by fuels for various systems.
189
TABLE 5 - Additional Input Data to produce KW, KWH and BTU x 10°
MEDSI INPUT DATA ■-«r».c -
Form No. 3 R«. 12/15/69 .HCENERGY »^W*'t/»pot . 'V'At
1.
BOILERS: Efficiency As Decimal at 100% Capacity .ITol
■ t
2.
Efficiency As Decimal at 10% Capacity .1 To 1
3.
KW Requirement Of Boiler Accessories
0
4.
HEATING PUMPS: Quantity (0, 1, 2, 3, Or 41
1
5.
Total KW Of Heating Pumps
6.
CHILLED WATER PUfUPS: Quantity 10, 1, 2, 3 Or 4)
y
7.
Total KW Of Ctiilled Water Pumps
8.
ABSORPTION REFRIG. SYSTEM: Total KW Of Accessories .
9.
CONDENSER WATER PUMPS: Quantity {0 1 2 3 Or 4)
/
10.
Total KW Of These Pumps
H
y
11.
TOWER FANS: Quantity (0, 1. 2, 3. Or 4|
12.
Total KW Of Tfiese Fans
3.3
13.
REFRIGERATION: MBH Boiler Input Per Ton At 100% Capacity . .
14.
MBH Boiler Input Per Ton At 10%Capacity . .
sv
ELECTRIC REFRIGERATION SYSTEM:
16.
CONDENSER WATER PUMPS: Quantity 10 1 2 3 Or 4|
rr
16.
Total KW Of Tfiese Pumps . .
Z.6C
17.
TOWER OR CONDENSER FANS: Quantity 10, 1 2 3 Or 41
18
Total KW Of Tfiese Fans
REFRIGERATION:
19.
KW Per Ton Input To Compressor At 100% Capacity . . .
1
20.
KW Per Ton Input To Compressor At 10% Capacity
1
21.
SUPPLY & RETURN FANS: Total KW ...
Do Supply Fans Run Continuously (1), Intermittently To Maintain
22.
Temperature In Heating Season (2), Or Not At All (3), In Unoccupied Hours .
IT
23.
EXHAUST FANS: Total KW
3
24.
LIGHTING: Total KW Demand
yao
25.
OTHER ELECTRICAL LOAD: KW Demand
/o
26.
KW/Hours During Occupied Hours
27.
KW/Hours During Unoccupied Hours
1
28
DOMESTIC HOT WATER: Gallons Per Day
29.
Numtier Of Days Per Week
30.
so
31.
Leaving Water Temperature
32.
Efficiency of Water Heater As Decimal ITol
.tlf
8 . Future
At the present time, utilities are doing most of the energy calculations as a part of utility sales
promotion. Because of the competitive nature of fuel supplies, design engineers will be required to take
more responsibility and to perform more of these calculations and evaluations. Medsi is available to
assist engineers in this work and will be improving and adding to its library of shared time computer
programs. The opportunity to evaluate other details of design with computer accuracy and speed re-
quire the progressive designer to develop skills in this area.
9 . Summary
The primary objective in developing these programs has been achieved. Medsi programs give
accurate answers with minimum manual calculation. The program and an application manual are avail-
able now to qualified subscribers.
190
TABLE 6 - Part Load Hours
SAMPLEI OFFICE BUILDING. MINNEAPOLIS DEC 1.
FIN TUBE RADIATION AT EXTERIOR. CONVENTIONAL RETURN
SYSTEM #1 WITH ECONOMISES
MULTIZONE OB DOUBLE-DUCT SYSTEM
HOURS OF PER CENT OF 70 TONS
80
75
66
50
33
85
20
10
TOT
JAN
0
0
0
0
0
0
0
0
0
0
FEB
0
0
0
0
0
0
0
0
0
0
HAR
0
0
0
5
0
0
0
0
0
5
APR
1
5
22
51
0
0
0
0
0
81
HAY
16
22
53
114
0
0
0
0
0
207
JUN
92
34
61
83
0
0
0
0
0
272
ML
136
31
43
77
0
0
0
0
0
286
AU6
134
33
42
62
0
0
0
0
0
293
SEP
46
26
52
92
0
0
0
0
0
217
OCT
8
0
47
60
0
0
0
0
0
137
NOV
0
0
0
14
0
0
0
0
0
IS
DEC
0
0
0
0
0
0
0
0
0
0
TOT
436
155
324
603
0
0
0
0
0
TOTAL
HOURS
OF REFRIG. REO'D.
.:
23
HOURS OF
PERCENT OF
893 MBH
60
75
66
SO
33
25
20
to
TOT
JAN
127
83
74
160
280
70
6
1
0
743
FEB
96
16
48
131
250
105
12
7
0
671
79
1 9
40
101
231
189
43
34
3
743
APR
30
22
28
60
9S
151
96
176
56
715
HAY
3
8
27
16
46
59
73
283
196
717
JUN
0
0
9
2
31
35
45
182
330
637
JUL
0
0
1
0
16
41
36
116
396
610
AUG
0
0
2
0
16
43
37
125
397
626
SEP
0
5
25
9
45
36
59
27 5
223
681
OCT
15
18
37
26
85
88
101
267
96
738
NOV
66
20
36
106
172
197
57
56
5
719
DEC
106
15
73
130
266
124
14
10
0
743
TOT
530
150
404
746
584
1S3S
TOTAL HOURS OF HEATING REQ'D .59
10. References
(2) U.S. Department of Commerce - Climates
of the States, for the State involved.
Superintendent of Documents, U. S.
Government Printing Office, Washington
D. ©. ,
(1) Engineering Weather Data , Depart-
ment of the Air Force Manual AFM
88-8, Chapter 6, Superintendent of
Documents, U. S. Government
Printing Office, Washington D.C.,
(3) ASHRAE Handbook of Fundamentals,
, Chapter 28. American Society
of Heating, Refrigeration and Air Con-
ditioning Engineers , Inc., 345 East
47th Street, New York
191
Figure 1 . Floor plan showing application flight heat to heat loss.
192
No Heat Gain Or Loss Through
Partitions And Floor ^
giTTTT
iimiiii
Retail Store
iii)iiiinmiiiiiMiMuiuihiiiiimi luiiiiiiiuniiiiiiiiiiiiiniiiiiiiniiiiiMiiii mi in
7
Roof-^
'^Lighting Fixtures^-^
Retail Store
Figure 2. Retail store with lights applying to all of heat loss,
193
No Heat Gain Or Loss From
Partitions And Floor~^^
'liMjjiui mm imiim iiiiimi iiiniiiiiiii \ ni il II 11 lllll I li li lllllHi I 111 111 II ill llilliigmT
"^^ Retail Store
[
Ho o o ("J"^
Fin Tube Radiation
mimiinillllTTTTTrWTTTT
Roof-^
5 5
©Exterior Zone 'fh^^ifnt!,®
^Thermostat Thermostat-^
Figure 3. Retail store with lights applying to some of heat loss.
194
196
197
198
The Program of the ASHRAE Task Group
on the
Determination of Energy Requirements
for
Heating and Cooling Buildings
K. H. Tull''"
Consulting Engineer
A description is given of the work being carried out by the ASHRAE Task Group
on Energy Requirements for Heating and Cooling of Buildings. The Task Group's work
is being done by four subcommittees. Subcommittee #1 is responsible for developing
methodology and calculation procedures for hour by hour determination of heating and
cooling loads . Subcommittee #2 has the task of developing a new calculation tech-
nique which will apply the heating and cooling loads to the equipment components and
determine the energy requirements. Subcommittee #3 has the job of combining load
calculation and system energy determination with weather data, building operating
schedule and other factors affecting system performance to develop overall annual
energy requirements of the building. Subcommittee #4 is responsible for instrument-
ing buildings to measure energy requirements and refine the calculation procedures .
A summary of the progress made to date is presented.
Key Words : Task Group on Energy Requirements , building energy requirements ,
calculating energy requirements .
1. Introduction
At the present time, for most engineers, the calculation of the energy required for heating and
cooling a building is more of an art than a science. The ASHRAE Guide and Data Book in Chapter 54 of
the Applications [1]^ volume describes calculation procedures which are not claimed to be exact but
which, based on experience and the application of good judgement, can give reasonably accurate estimates
for residential buildings . Not even this limited claim is made for any calculation procedure for
commercial and industrial installations. A single paragraph on page 656 covers the subject and plainly
states :
"To properly evaluate the energy requirements for commercial and institutional buildings, it is
necessary to establish the character of all thermal load sources, the resultant magnitude of each of
these specific heat release mechanisms, and their relationship to the most effective method of load re-
moval. A thorough analysis of both the total energy balance and the character of the system operating
cycle must be made in order to accurately establish the energy requirements for each specific building".
This statement may be a good general description of the problem, but it provides little help to the
engineer faced with determining the energy requirement for his specific building.
Yet the accurate determination of the energy required for heating and cooling a building is one of
the most important, and also one of the most difficult problems for the air conditioning engineer. It is
important because the energy cost is an essential and significant element of the building's overall own-
ing and operating cost. Accurate or not, it may be the determining factor in the selection of the air
conditioning system or the energy source for a new structure. The problem is difficult because of it's
complexity. It involves not only an accurate determination of the heating and cooling loads, taking into
account the varying influences of the weather and the building operating schedule, but the even more
complex problem of determining the performance of the heating and cooling system under varying conditions
of partial load. The complexities of the problem have led to solutions based on approximation, experience,
judgement, rules of thumb, judge factors, or just plain guess.
In recognition of the need for ASHRAE to develop better engineering information on this subject, a
Chairman of ASHRAE Task Group on Energy Requirements for Heating and Cooling Buildings.
Figures in brackets indicate the literature references at the end of this paper.
199
Presidential Committee on Energy Consiamption was established in . This committee reviewed the prob-
lem in considerable detail and then, typical of Presidential Committees, recommended the appointment of
another committee, a special Task Group, under the Research and Technical Committee, to "develop accurate
methods for determining annual or seasonal energy requirements for heating and cooling, taking into ac-
count all energy sources and all sizes and types of buildings".
The original Task Group carried the analysis of the problem further until the resignation of the
chairman at the end of . The Task Group as presently organized met first in March . It has
been meeting on a schedule of about two days every two months since them.
At our first meeting it was recognized that other engineering groups were already working on new
load and energy calculation methods based on computer techniques. It was decided to take advantage of
this work, in so far as possible, in the development of the ASHRAE calculation procedures. Subsequently,
several organizations, particularly the National Bureau of Standards, the Post Office Department and
the National Research Council of Canada, have contributed to the Task Group's program.
The work of the Task Group is carried on by four sub-committees. A description of their assignments
will outline the plan of operation being followed.
Subcommittee //I on Heating and Cooling Load Requirements is responsible for developing the methodol-
ogy and calculation procedures for determining Heating and Cooling Loads for energy calculations.
Subcommittee #2 on System and Equipment Energy has the task of developing a new calculation technique
which will apply these heating and cooling loads to the equipment components of an air conditioning system
and determine the corresponding energy requirements.
Subcommittee #3 on the Overall Logic Pattern has the job of combining the load calculation and the
corresponding system energy determination with the weather data, the building operation schedule, the
requirements of auxiliaries and any other factors affecting the system performance, to develop the over-
all annual or seasonal energy requirements of the bulding.
Subcommittee #4 on Field Validation Studies is responsible for plans to instrument one or more
buildings which will be used to refine and validate the energy calculation procedure.
The whole Task Group periodically reviews the work of each subcommittee to provide coordination and
direction for the total program.
2. Calculation Procedures
The first step in such an energy calculation program is obviously the development of an accurate
heating and cooling load calculation procedure. Taking advantage of computer capabilities it is now
possible to work with more sophisticated calculation procedures and gain in basic accuracy as well as
speed. It was decided at the beginning of the program to take fullest advantage of the newest calculation
concepts, which require the use of computers, in order to make the ASHRAE procedure the most advanced
possible .
For accurate energy calculations a continuous, or hour-by-hour calculation of the building heat
transfer, instead of the conventional, single point, design load calculation, is necessary'. The heat-
ing and cooling energy requirement responds to the everchanging dynamic heat loss and gain of the build-
ing as it is influenced by the continually varying outdoor air conditions, the position of the sun, the
cloud pattern and wind effect, and by the operation schedule and the heat generating characteristics of
the building. The air conditioning system responds to this changing load as it appears inside the build-
ing and is picked up by the heating and cooling distribution system.
The current methodology of design heat load calculation presented in the ASHRAE Book of Fundamen-
tals () [2] has to be modified for the hour -by-hour load calculations, especially with reference
to the transient thermal response of the building structure to the outdoor weather conditions and changes
in internal space temperatures. The total-equivalent-temperature-difference concept employed in the
Book of Fundamentals is only applicable as long as the hour-by-hour pattern of weather conditions re-
peats prescribed design cycles. The actual weather pattern, however, is puite random, or non-steady
periodic, so that the design equivalent-temperature-difference concept is not valid for a real weather
situation.
A new methodology, called the Thermal Response Factor Technique is better suited to the calculation
of non-steady periodic heat transfer. The application of this technique to cooling load calculations was
proposed by Stephenson and Mitalas [3]. The ASHRAE Task Group adopted this new methodology for calculat-
ing the transient heat transfer of exterior walls and roofs, and to some extent, the heat storage effect
of the internal mass of the building. The subcommittee on Heating and Cooling Loads has completed
development of a new calculation procedure based on this technique which will be used as the basis for
our energy requirement calculation. '
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The details of this load calculation procedure were first released for limited distribution to engin-
eers working in this field in June at the ASHRAE annual meeting at Lake Placid [4]. Comments,
criticism and suggestions were rec^uested and these were reviewed in a Forum at the January ASHRAE
meeting in Chicago. On the basis of these comments, and some further work by the subcommittee, some
revisions have been made and a revised version has been prepared for general release. This revision in-
cludes an interesting and valuable short cut procedure which will considerably reduce the computation
time involved. Instead of calculating each category of load for all hours of the year, it has been
found practical to develop combined response factors for the whole building, or for a zone, based on
approximately 100 hours of the year. Then the combined response factors can be used for a very rapid
calculation for the total hours. This technique has been tested at the Bureau of Standards.
The output of this load calculation will be the hour-by-hour heating and cooling loads to which the
air conditioning system responds. We know of no present calculation procedure that attempts to accurately
translate this load, through the system performance characteristics, into the system energy requirements.
At this stage all calculations resort to some approximation procedure to relate the heating and cooling
load to the partial-load performance characteristics of the system. Such an approximation has been
essential because of the tremendous complexity of any more rigorous determination.
Here again the availability of computer capability and new calculation techniques presents a chal-
lenge arid an opportunity to develop a new methodology. Rather than attempt to refine present approxi-
mation procedures, the Task Group decided to take a more fundamental approach. The subcommittee on
System and Equipment Energy is developing a new system-simulation technique which will make it possible to
calculate the response of the complete system to the hour-by-hour load changes. It is believed that this
new technique will open the way to improved methods of evaluation of heating and air conditioning systems
and their controls. This work is in the early development stage. Sample simulation techniques have been
developed for some typical systems. Other systems and system variations and a generalized simulation
procedure are now being developed.
A bulletin covering the preliminary work of this subcommittee was released for limited distribution
in June [5] at the ASHRAE meeting in Denver. Comments on this procedure were reviewed at a Forum
in January . Further work on this technique is now underway looking toward the release of a revised
and more complete bulletin.
3. Overall Logic Subcommittee
The work of the subcommittee on the Overall Logic Pattern will begin in earnest when the system
simulation procedure is well in hand. We can, however, already visualize some of the problems involved
in bringing this whole program together into a unified calculation procedure. One of the major problems
is related to weather data. The heating and cooling load calculation for this procedure requires the
coincident hourly readings of dry-bulb temperature, relative humidity or dewpoint or wet-bulb temperature,
wind velocity and direction and direct and diffuse solar radiation. Further, the performance of many
system components is related to these same outdoor weather parameters. Existing ASHRAE weather data,
which covers only Design Load weather conditions, are clearly unsuitable for the needs of this procedure.
The Task Group is working with the ASHRAE Technical Committee on Weather Data to obtain the necessary
data in the form needed for this program.
Another weather problem is the determination of a typical year for use in calculating predicted
energy requirements. Out of ten or twenty years of weather data, how does one determine what a typical
year would be for calculating energy requirements and operating costs? ASHRAE has sponsored two research
projects aimed at eventually providing Typical Year Weather Data for a number of locations. One of
these projects follows what might be called "conventional, meteorological approaches". Loren Crow
has made a study of the weather at one location and by the "scientific and careful use of meteorological
factors" has developed a typical year's weather data made up of 12 typical months, each selected to
bring it within acceptable tolerances to the long-term average condition and the total climatic range
for that particular month.
In a parallel project with the same ultimate objective, Z. 0. Cumali is developing a mathe-
matical analysis of the weather data at the same location to determine if it is possible to develop
mathematical relationships whereby a typical year's weather data, including all the variables needed in
the energy calculation can be generated within the computer as a part of the load calculation procedure.
This unconventional approach shows distinct possibilities and indicates long range benefits in other
areas of weather information.
Subcommittee #3 is made up of engineers who are regularly working with and operating computer pro-
grams for determining energy requirements. It is in effect our user's committee and provides a very
valuable and practical viewpoint and criticism of the theoretical work of the Task Group. Since this
subcommittee represents at least seven of the most advanced computer programs used in the United States
today, it provides a unique opportunity to check the calculations of these programs against each other.
To do this a project called "Operation Cross Check" is being carried on in which all of the programs
calculate the same building using the same input information. The results are then analyzed in consider-
able detail to evaluate program differences. The understanding gained from this project will provide
201
an invaluable input in helping to standardize the ASHRAE calculation procedure.
We can see ahead that this energy calculation procedure is going to require more information on the
partial-load performance of some system components than is ordinarily available now. Moreover, we can
see that this information will be needed in forms suitable for use by the computer. It is commonly
recognized that all heating and air conditioning systems only operate at their design of full-load con-
dition for a very few hours each season. Most of the operating hours are at varying partial-load condi-
tions, significantly different from full-load. To determine the system response to these partial-load
conditions we must have data on the partial-load performance of the system components. Moreover, for
optimum use in the computer program, this information is needed in equation form suitable for use by the
computer. A preliminary step in setting up this kind of performance information was taken by subcommittee
#2 in the bulletin released in June [5]. This bulletin included examples of the equation forms
proposed for expressing performance information of the major components of the system.
The Task Group is now requesting manufacturers to provide such information. At the ASHRAE meeting
in San Francisco, the Task Group requested the Research and Technical Committee and the Board of
Directors of the Society to approve a statement setting forth this future requirement for component
partial-load performance information. Responding to that request the attached statement was approved.
The need for this information has also been recognized by the members of APEC and that organization is
also urging manufacturers to provide this kind of performance information.
We see this as the beginning of a long range and long term program to revise the performance infor-
mation issued by manufacturers on the system components they manufacture. We believe that the ready
availability of such information is essential for the future, more accurate, calculation of building
energy requirements.
4. Field Validation
Subcommittee #4 on Field Validation Studies has the responsibility for setting up and conducting
one or more field tests on actual buildings to validate and, or, refine the overall calculation procedure.
This program is considered too complex and too vital to the interests of the Society and to the engineer-
ing field to be released as an ASHRAE approved procedure without a well supervised field check.
The field study plan proposes to set up instrumentation in one or more buildings which will measure
the local weather and other inputs required for the calculation. Each building will then be set up on
a computer by the local research contractor, using the calculation procedures developed by the Task
Group. Then each month the measured input data will be processed and the calculated energy requirement
will be checked against the actual, measured energy use of the building. It will be the responsibility
of the local research organization to analyze the monthly data and, working with the Task Grour , refine
and validate the calculation as indicated.
As a first step in this program, four test sites were selected and preliminary studies wure made to
develop the costs of instrumentation and carrying out the proposed two year test program. At the ASHRAE
meeting in San Francisco, in January , the Research and Technical Committee recommended, and the
Board of Directors approved, going ahead immediately with the field test program at one site, the one
at Ohio State University in Columbus, Ohio.
The work of the Task Group has already indicated areas where present ASHRAE engineering information
is inadequate. Through the Director of Research, the Task Group has requested that research studies be
undertaken in the following areas:
1. An up-to-date determination of the energy distribution from lights, including the effects of
thermal storage.
2. A study of the effects of moisture absorption within the conditioned space on the cooling loads;
i.e., the effect of latent heat storage on the latent cooling load.
3. A study of the transient heat transfer response of walls, ceilings and floors, including
non-homogenous sections .
4. Guidance from weather experts in establishing typical year weather data.
5. A study to relate reported cloud cover to solar radiation.
5 . Summary
The work of this Task Group is considered by many responsible members of the Society to be one of
the most important and far-reaching undertakings of the Society. Based on it's work we now can make
heat-loss and heat-gain calculations which adequately and accurately reflect the actual transient heat
flow due to the varying outdoor weather and also the varying indoor space temperature and load conditions.
Through the thermal response and weighting factor technique we can take into account the heat storage
effects of the structure and determine the hourly, actual heating or cooling load imposed on the heating
and air conditioning system. By means of a general simulation technique we then expect to be able to
202
calculate the system performance based on the performance characteristics of the system components. This
will not only allow us to more accurately predict the operation of a given system and determine it's
operating cost, it will provide a calculation basis for design optimization studies of both the structure
and the heating and air conditioning system. Other forward looking engineers see the work of the Task
Group as laying the foundation for more accurate and comprehensive computerized control of the heating
and air conditioning systems of large buildings, with resultant significant savings in operating cost.
As for the Task Group, we have our work cut out for us for sometime ahead. The revised bulletin
on load calculations has been released within the last few months [3]. Within a year we expect to re-
lease a revised bulletin covering the work on system-simulation and component and system energy calcula-
tions [5]. Our work will then continue on the field test programs and in efforts to improve, simplify
and refine the procedure. We expect this program to generate other research activities, within and
outside Society, as it has already done, to develop the engineering information needed for the program.
Hopefully, as a result of all this effort on the part of a dedicated group of Society members, we
can look forward to the day when air conditioning engineers can precalculate the performance of their
system designs and determine the energy requirements with confidence and accuracy, based on standard
ASHRAE calculation procedures.
Appendix A
A prediction of the energy required to operate the heating and air conditioning system of a build-
ing is essential to a complete and realistic evaluation of a heating and air conditioning system design.
Such a prediction requires not only an accurate calculation of the heating and cooling loads but also
a determination of the response of the H & AC system to those loads as they vary with the weather and
with the changing conditions of building operation.
The ASHRAE Task Group on Energy Requirements for Heating and Cooling Buildings is developing
calculation procedures to accurately determine and predict such system energy requirements. The Task
Group program is being carried out under the supervision of the Research and Technical Committee in res-
ponse to a specific authorization of the Board of Directors of the Society.
An essential element of this calculation procedure is a determination of the energy requirements
of the various system components in response to the partial load conditions under which they operate.
The performance information presently available on many system components Is Inadequate for such a
determination. In addition to the performance information normally provided for equipment selection at
design load conditions, performance data are required covering the partial load conditions under which
the components normally operate. To facilitate the use of this information in computer calculations,
it is desireable for these data to be expressed in equation rather than tabular form.
The Task Group on Energy Requirements is requesting that equipment manufacturers move as rapidly
as possible to provide such information in this form. It further requests all ASHRAE Technical Commit-
tees to work with the manufacturers and the Task Group in developing this information.
6. References
1) ASHRAE Guide and Data Book ( Applications)
2) ASHRAE Handbook of Fundamentals ()
3) Stephenson, D. G. and Mitalas, G. P., "Cooling
Load Calculations by Thermal Response Factor
Method". ASHRAE Semi-Annual Meeting, Detroit,
Michigan, January , Paper No. .
4) Proposed Procedure for Determining Heating and
Cooling Loads for Energy Calculations, Edited
by M. Lokmanhekim. ASHRAE Task Group on Energy
Requirements for Heating and Cooling, .
5) Proposed Procedure for System Simulation, Edited
by W. Stoecker. ASHRAE Task Group on Energy
Requirements for Heating and Cooling, .
203
Successful Applications of Energy Analysis Programs
K. M, Graham
Southern California Gas Company
Los Angeles, California
The lessons learned in bringing several environmental computer programs to a
successful operating state can be used to make this process easier for others.
Several suggestions such as attempting to make operations as foolproof as possible,
allowing for development time, documenting data and creating a set of accessory
packages should be beneficial to others when they first implement their new
programs. The mistakes of oversimplifying and over complicating several different
environmental programs have proven that a good engineering assessment of the time
context and data available are essential in the successful application of these
programs. In the successful use of several in-house developed programs, G.A.T.E.
programs, and A. P. E.G. programs, each has always required considerable initial
effort. The use of approximation techniques is essential as experience is gained.
The use of the "Sol-Air" method used in the A.P.E.C.-H.C.C. program with the
G.A.T.E. energy analysis is one example of such approximating techniques. These
experiences, which have been gained over a period of years, should prove valuable
to anyone involved in making an environmental program operationally successful.
Key Words: A. P. E.G. programs, energy analysis programs, environmental
computer programs, G.A.T.E. programs, Sol-Air, approximating techniques.
The key to most successful operations is experience. We all want to be immediately successful in
all things, but unfortunately we are not. This is especially true with new computer programs in the
field of environmental control. The first few times one works with any new computer program might be
compared to the first few times a laborer attempts to work a new kind of hand tool. It takes time to
learn how to be effective. The amount of time depends upon many variables including the knowledge
available from others who have experienced a similar process.
In the last few years, we have had the opportunity to analyze and work with many computer programs
associated with environmental control. As a result of this experience, the following suggestions can
be made:
1. Make all operations as simple and foolproof as possible. Most people are short tempered
when trying to understand someone else's work. When something doesn't work easily, people
naturally assume it is someone else's fault. Programs will not be successful if you assume
that everyone else has your intelligence and patience. No one really cares that the reason
your program is considered useless is because people were stupid in the way they applied it.
You will be the one blamed simply because the program was unsuccessful. It is up to you to
insure against this. Use charts and graphs plus plenty of redundant information whenever
possible. Keep input data and the calculations for input data to a minimum. You'll be
surprised that often when you aim the operating procedures so that they can be performed by
idiots, people will claim that you are a genius. If you aim your operating procedures toward
geniuses, many people may claim that you are an idiot. We will see later how charts and
graphs can be used to easily collect what might otherwise amount to rather extensive data.
2. Allow for plenty of time. Experience indicates that if a time limit is imposed that might
be restrictive that that time limit will almost always be exceeded. In fact, it seems the
more desperately something is needed,, the more certain you can be that a good printout cannot
be obtained on time. There is a good scientific explanation for this phenomenon. The
successful application of a computer program requires many successive operations. Each
of these operations like correctly filling in the data sheets or having a computer in running
condition when you are ready, will not cause any problems nine times out of ten, but when
taken in successive steps Baye's Rule of Probability takes effect. We know from Baye'sRule
Energy Systems Sales Supervisor
205
that if only seven steps were required, each being 90% certain of being done correctly, that the
overall probability would favor an incorrect computer run. This Is because the total probability
is the product of each step's probability. In your enthusiasm to successfully apply a new
program, always allow for plenty of time. Nothing else but time and experience can be used
to reduce the number of operations and the chances of error to a minimum. It is far better
to do without than to try a program in a critical situation which has to be resolved in a
limited time. People can become very bitter with a program which fails them in their first
involvement. Early users must understand that some experience is necessary before definite
time commitments can be made. Even then it is wise to allow for plenty of insurance time when
making your time commi hnents.
3. Be certain of your data. So many different numbers are used in an environmental program
that it IS extremely easy to forget which units are being used and how these numbers and units
relate to the calculations in a program. One of our first steps when working with new programs
is to add units and explanatory remarks right into the printout. Often the originating pro-
grammer is so familiar with the program that he forgets that these numbers can be very difficult
for others to understand. Another device which adds certainty to your data is intermediate
printout of calculations. In other words, before summing key calculations, provide an
intermediate printout. This is a great help in the successful application of a program because
usually the user does not have the programmer's ability to dump the whole program in order to
look for why a calculation went wrong. A user also is more confident in a final answer if
all the component parts of that answer appear in the printout and seem to be of the right
magnitude, if they are not of the right magnitude, it makes it easier for him to trace down
which input data applies so that it may be reanalyzed. These precautions may seem like a lot
of drudgery compared to developing the logic which is the heart of the program, but the
greatest program in the world isn't worth anything to others if it can't be successfully
applied to solve their problems. Make the input and output data easy to understand.
4. Provide a good program package. A real key to any program's successful application is in
having a good package for it to operate in. All sorts of provisions which can help a user
successfully apply a program are often neglected when a program is given to a user. A good
documentation in both common english and the language of the program can save the user much
anguish. The user should have good records of the control cards needed and other data which
relate directly to the use of the program on his particular computer. As soon as is practical,
at least two copies of the program should be made for insurance purposes. Plenty of clearly
labeled folders and covers for input data and printouts also need to be provided. Without
these labeled devices, soon all the input data and printout data from various projects can
get mixed. This can lead to some frustrating situations, especially in multiple runs of the
same project. A little effort to insure that the program will be operated within a well
managed and equipped package is well justified.
One of the ways we learn is by mistakes. Some of our mistakes were costly and time consuming. It
is hoped that a discussion of them will help others in avoiding these pitfalls. The first environmental
energy analysis program we worked with was probably one of the world's worst applications of the
computer. This program was basically a set of imperical formulas and rules of thumb that had come from
various sources. Some of these formulas were obtained from generalized experience, some from prejudice
or pure myth. Instead of capitalizing on the computers capabilities to handle large amounts of data
and many calculations, we simply had a program which made the same mistakes we made in hand calculations,
only faster. This program was very unsatisfactory. Rules of thumb have their place when related to
human judgment but some very strange answers can develop when they are unmercifully applied by a
machine. This program was discarded soon after it was developed.
Our next program was more scientific and in fact was a series of programs. The first in this
series was a program which determined the energy requirements of a facility hour by hour for one year.
Once this data had been obtained, it was given to a second program which contained equipment char-
acteristics and calculated the amount of gas and electricity various systems would require in order
to heat and cool a building. The third program was simply a rate cost program which solved for the
cost of gas and electricity used. This annual cost data could then be compared to the initial cost
for an economic analysis of which system offered the best investment to a potential owner.
We made many mistakes with this program also, almost all of which were related to the input data
for the first program in the series, the energy requirements program. We found that we had limited
data which could be given to the program. As a result, the program did not accurately reflect the
real requirements of many facilities. Basically we tried to obtain the input for this program from
the heat load calculations done manually by the consulting engineer. For the entire facility, we
broke the calculated heat load into time dependent loads and temperature dependent loads. The
computer could then take each of these loads plus a time schedule and temperature schedule and produce
an approximation of hour by hour energy requirements.
206
The time dependent loads wb re basically the solar component, the people component and light com-
ponent of the heat load, fach of these loads described in a profile format of how they varied hour
by hour for different day types was provided as input data. (See fig. I and fig. 2)
The temperature dependent loads were transmission, outside air (both sensible and latent) plus
infiltration. Each of these loads were given at at least two different temperatures in order to
provide a method of linear interpretation for loads at other temperatures. (See fig. 3)
As you might guess, this type data was far better than a rule of thumb approach but still was
rather gross. In most facilities, a significant load is found from the effect of zoning. Many times
both heating and cooling are going on simultaneously creating an artificial internal heat load. Some
distribution systems deliberately mix heating and cooling energy under certain conditions. We call
this artificially produced load balance or trim heat. Transmission through walls of any real thickness
is not strictly linear. Latent outside air loads are wet bulb dependent, which was not being accounted
for. The solar load is affected by clouds and adjacent buildings which had also not been accounted for.
We made our biggest mistake at this point. We decided to have a program written which took into
account every possible factor which we thought would effect a building's energy requirements. This
awesome task was undertaken by Southwest Research Institute for 25 member gas utilities and the result,
after many years work, was known as the G.A.T.E.^ long form program. This program was fantastic. It
took into affect temperature of street water, leakage around air handler coils, every control setting
in the building, wind direction and speed, and every other conceivable piece of data which might affect
the building's energy requirements.
Although this program was technically excellent, operationally it was a great mistake. We found
that the data needed by the program was not usually available until the building was well under con-
struction. By that time, the answers it provided were of no practical use as most of the decisions
which these answers would effect had already been made. If we assumed and guessed at input data at
an earlier date in construction, we found that so many variables had such wide error margins that the
resulting data in many cases was meaningless.
Upon discovering this dilemna, we gave a lot of thought to how we might ever obtain a successful
Energy Analysis Program. There seemed to be a paradox. By the time accurate data was available, the
decisions which might be affected by that data had already been made.
We now realize that our mistake was in the degree of accuracy which we were trying to obtain.
The computer can be so very accurate, it is hard not to try to obtain all the accuracy that is
available. But practical engineering tells us that ground temperature and air-handler leakage usually
have little effect compared to major loads like outside air temperature and solar radiation. We can
usually determine the following major loads to within plus or minus ten percent at a relatively early
stage of construction:
1. Transmission heat load
2. Outside air sensible heat load
3. Outside air latent heat load
4. People sensible and latent heat load
5. Lighting heat load
5. Solar heat load
7. Distribution system balancing heat load
These loads are sufficient for us to obtain data upon which practical decisions can be made. A
program starting from this data coupled with the data available from a year's weather data from the
U.S. Weather Bureau provides a pretty good picture of the facilities energy requirements. The Weather
Bureau data use has hour by hour records of dry bulb temperature, wet bulb temperature, cloud cover
and other factors which might affect these basic loads. This data like the other data may only be
within ten percent or so of what any future weather year will be like.
When we had settled upon a ten percent or so allowable error, we found that the program became
very much more workable. Users could provide answers that were in this range from rough calculations
and experience. We also limited ourselves in most cases to the outside shell of the building which
greatly simplified matters. The effect of zoning and other internal imbalances was then loaded as a
^Group to Advance Total Energy, Inc.
207
function of the type distribution system plus whatever the designer's experience indicated. This saved
many very complicated calculations that otherwise would have been required for this relatively small
load. We also carried loads forward as stored heat when equipment capacity had been exceeded. A
simple calculation allowed us to also determine the drift from inside design temperature when stored
heat was in effect. Once we had settled upon a lesser degree of accuracy in our input data, we found
that we actually had not given up much at all. When compared on the same building, we found one
program gave answers within five percent of the other. In addition, when it came to using this data
to select systems, every system compared in exactly the same relationship in either program.
This program was initially known as the G.A.T.E. APPROX program. For the last year, the old long
form program has been dropped and the newer program is now the official G.A.T.E. program. We have run
this program well over 100 times in the last year and found that it can provide very meaningful data
concerning the use of various energy systems in all types of buildings.
We took this program and worked hard at making it as operationally successful as was possible.
We simplified the input data and printout into an easily understood format. We allowed for plenty of
time when making studies. We also built up a good package of accessories to insure good management
of the program. For example, rather than collect data directly on key punch sheets, we used the forms
in the figures at the end of this paper for ease of understanding. Later we transferred this graphical
data to input sheets as numbers and reproduced it in that format in the printout.
We still had an occasional timing problem. Often decisions are made concerning a facility even
before the basic heat load calculations have been done. The consulting engineer usually will not
start his calculations to determine the component heat loads needed by the G.A.T.E. program until plans
are fairly firm. Yet decisions whether to use a central plant or to use gas or electricity as an energy
source might be made before that time. Sometimes a consulting engineer has not even been retained when
these basic decisions are being made. We found that we were having to do many heat load calculations
ourselves. This caused us to become interested in an organization known as A. P. E.G. We joined
A. P. E.G. and began using their H.C.C. program which provides heat load calculations from the basic
plans of a building. Again we had many start up problems, but each time we found it a little easier to
bring a program to an operational state.
We now are in a position to obtain the data necessary for decisions on building energy systems at
a very early stage. We can even do a fair job of approximating energy requirements from as little data
as a plot plan and an artist rendering. These give enough physical data in conjunction with other data
we have gained from past experiences to begin a preliminary study. As new data becomes available at
later dates, the study can be updated as required.
A surprising bonus developed out of our work with the A.P.E.C.-H.C.C. program. We found that this
program could not only describe the hour by hour load from solar radiation quite accurately, it could
also calculate the non-linear portion of transmission and handle the effect of hour averaging. These
calculations are quite sophisticated, but can be done by the computer. The results provide far greater
accuracy than is usually provided by manual calculations. This fallout has provided us with a solution
to a very perplexing problem. We knew that a better heat load calculation method would be possible if
we used the "Sol-Air Method" as described in the A.S.H.R. A.E.^ Guide. The use of the "Sol-Air
Method" allows for the consideration of the dynamic nature of heat transfer in a building. This method
is used in the A.P.E.C.-H.C.C. program for a 24-hour day but it is very difficult to use for a
hour year-long energy analysis. We were neglecting this effect in our energy analysis and using only
linear relationships for our temperature dependent heat loads. Through a modification to the A.P.E.C.-
H.C.C. program, we are able to extract the non-linear portions calculated when using the Sol-Air Method
for a typical day for each month of the year and then we created a time profile of these non-linear
components of transmission loads in an hour by hour printout. What we actually did was add a step to
the A.P.E.C.-H.C.C. program which calculated what the transmission would be on a straight linear basis
and then subtracted this quantity from the more sophisticated quantity calculated using the "Sol-Air
Method" and hour averaging. This represented the hour by hour differences for a typical day in one
month. The A.P.E.C.-H.C.C. program was also looped so that we obtained an hourly table of typical days
differences for each month of the year. In other words, we are approximating a very complex temperature
dependent load into the G.A.T.E. program as a more simply handled time dependent load. This is only an
approximation of what is really happening but it has proven to be a satisfactory way to handle this
complex load. In the energy analysis program, we adjust the hour by hour data calculated without using
the Sol-Air Method by the total correction factor derived for that hour by the modified A.P.E.C.-H.C.C.
program for a typical day of each month. In practice, since the G.A.T.E. program requires an hour by
hour solar table for typical days of each month, we simply have the A.P.E.C.-H.C.C. program add the
solar and non-linear component of the transmission load together before printing our a yearly table of
these values. (See fig, 2)
'Automated Procedures for Engineering Consultants, Inc.
^American Society for Heating, Refrigeration and Air Conditioning Engineers
208
With continuing experience, our capabilities continue to grow. We have learned how to make haste
slowly and not to expect too much too soon with new programs. We have also learned that in order to be
successful, we need to truly have a good understanding and feeling for the data that we are dealing
with and have a system to manage and contain our work. The overall result is the successful application
of these programs, but we had to learn many lessons first. It is hoped that some of these lessons
will be helpful to you in your applications of environmental control and energy analysis programs.
209
Thermal Loads:
(Each day type must be described. Number functions in each
graph by day type rwmhex .) ft titifjffmS , A' *vetr^yS
Heat from electrical appliances (primarily lights) :
@ 100% = il&SQ—MBtu ^ s wArn/ftH x 835.? /Ct4/
xuu
SO
80
B
3
e
70
X
60
ffl
S
50
>(-i
40
o
30
20
10
0
6> 3.«#aMW/ifH/» ^^s/?
i
1
\
-H
[
1
i
i
1-
:
i
r J
1
M
i
1
i
i
i
1
i
i
j
j
j
■
— f-"
—
i
I
■ y
1
\
1
1
■
■
!
i
j-
i
.1
12 34 56 78 91D 11 34 56 78
AM PM
TIME OF DAY
Heat from people:
/OO NU^US & ISO *
100
90
80
70
60
S 50
o
VP
5v
40
30
20
10
0
i !
■ 1 1 '
!
1
...
—
i
_. __
■
—
-_
....
I
1
:
T
■
H
■ 1
i
1
1
....
i
.....
....
...
j .
.....j...
12 34 5 678 9 10 5 6 78 12
AM PM
TIME OF DAY
Figure 1. The form used for collecting data regarding time dependent heat loads from people and from
lights with example data filled in.
210
Heat from Other internal sources: (Lt^tOfitn^^/ 8VdtJf^S*'F(*^^^^)
@ 100% =
MBtU
100
90
80
70
60
50
40
30
20
10
0
1
1
'1
i
. . j ; 1
1
i
j
1
1
1
i
: 1 ' i
- : 1 i
1
j
1
r
1
— 4
i
■ [■ . -
1
■1
j-:-
. 1
.
i
n
1
1 —
1
-H
)
1 23 4 567 8 9 10 11 12 12 34 56 7 89 10 11 12
AM PM
TIME OF DAY
Heat from solar radiation:
@ 100% = MBtU
(The percentage solar radiation by hour at 34° latitude for a
facility of uniform sides has already been included in the
program- If actual conditions will be greatly different from
this, please note below.)
Time
Dec
Jan -Nov
Feb -Oct
6
0.000
0.000
0.000
7
0.000
0.086
0.495
8
0.581
0.698
0.857
9
0.857
0. 906
0.988
10
0.970
0.980
0. 989
11
0.999
0.989
0.963
12
0.984
0. 979
0. 92 9
1
0.999
0. 989
0. 963
2
0.970
0.980
0.989
3
0.857
0.906
0.988
4
0.581
0.698
0.857
5
0.000
0.086
0.495
6
0.000
0.000
0.000
Mar-Sep Apr -Aug May- Jul June
0
.000
0
.435
0.
662
0
.733
0
.689
0
.867
0.
959
0
. 980
0
.966
1
.000
1.
012
0
. 990
1
.001
0
. 959
0.
905
0
.887
0
. 918
0
.824
0.
710
0
.680
0
.815
0
.653
0.
507
0
.457
0
.778
0
.573
0.
368
0
.353
0
.815
0
.653
0.
507
0
.457
0
.918
0
.824
0.
710
0
.680
1
.001
0
.959
0.
905
0
.887
0
.966
1
.000
1.
012
0
. 990
0
.689
0
.763
0.
959
0
.980
0
.000
0
.435
0.
662
0
.733
Figure 2. The form used for collecting data regarding time dependent heat loads from sources other
than people and lights plus data regarding the solar heat load with example data filled in.
211
Temperature Dependent Variables:
All temperature dependent variables are assumed to be linear. At
least two points are needed to define a straight line and there-
fore to describe any single temperature dependent variable. Up to
five different points may be used to describe all the variables
being considered.
(§) Design
Heating
* d Inside
Design
*
(§) Design
Coolinq
Dry Bulb
Temp. (°F)
Dew Point
Temp. (°F)
( )** 1
Transmission
(MBtu)
o
Outside Air
Sensible (MBtu)
o
Outside Air
Latent (MBtu)
0
0
Balance or Trim
Heat (MBtu)
0
o
Other Heat
Loads (MBtu)
0
0
* If an economy cycle is used, each temperature point where the
outside makeup air percentage is changed must be described.
** Leave blank and make outside air latent equal to zero in these
columns if humidity control equipment will not be used when
heating.
Air Handling System Size = \L^,QOd CFM S> ifOO C, f: /H. /7QN
Outside Air Makeup Rate = % = OOC C F, &I >
Installed Heating Capacity = ^X^^ MBtu® HS QTU/FT^
Installed Cooling Capacity = i/j^Q Tons
Heating System Shutoff Temperature =
Cooling System Shutoff Temperature =
Figure 3. The fom used to collect data regarding temperature dependent heat loads and data regarding
the equipment system used with exanple data filled in.
212
Comparison of a Short Form Load
and Energy Program with the Detailed
Westinghouse Load and Energy Programs
B. G. Liebtag and J. R. Sarver P. E.''^
Duquesne Light Company Westinghouse Electric Corporation
Pittsburgh, Pa. Pittsburgh, Pa.
Comparisons have been made between two heating and air conditioning load and
energy programs. The purpose of this comparison was to determine the proper ap-
plications and usefulness of these programs. Using the same input data necessary
for each program, typical buildings were analyzed by both programs. The results
of these programs were then compared to determine the accuracy of the short form
program. Each building was divided into the required number of zones. The re-
quirement being that each zone had the same basic physical and operating character-
istics. The short form program is basically a computerized A.S.H.R.A.E. Guide [1]^
method of load calculation. The energy calculations are handled with a modified
heating degree day method and an equivalent full load hour method for air condition-
ing. These modified methods allow for the evaluation of internal heat gains from
lights, people and equipment. The load section of the Westinghouse Electric
Corporation's program uses the thermal response factor method of calculating the
loads on the structure. These loads are determined on an hourly basis. The energy
program can use any defined weather year and will calculate the energy requirements
for all the building functions for each hour of the year. The results of these
hourly calculations are then summarized to give the annual energy requirements of
the structure. The final results indicate that the short form program can be a
useful tool for the engineer in properly evaluating building environmental systems.
The results also indicated the advantages of using the more detailed program for
larger structures.
Key Words: Electric heat, load profiles, control set points, ASHRAE method,
degree day approach, equivalent full load hours.
1. Introduction
Only in recent years since electric heat has made an impact as a practical method of heating a
building has it been necessary to properly estimate the annual energy requirements of a building. Many
times the need for an accurate estimate must be made long before final plans of the building are com-
pleted. In fact, in order to properly utilize the various advantages of the available fuels, the
decision as to which fuel is to be used must be made while the architect is doing his early stage plan-
ning.
Very accurate and elaborate computerized methods of predicting the energy consumptions for a pro-
posed building have been developed in the past five or six years. One of these methods is the West-
inghouse Electric Company's energy program. The program is divided into three sections. Section one
is a load model into which you feed the building characteristics, hourly environment specifications,
and actual hourly weather records. From this input data the program prints out the hourly zone load
profiles. Part two is the mechanical supply system design. From data obtained from part one the
Sjfinior Heating and Air Conditioning Engineer and Construction Systems Engineer, respectively.
Marketing Services Department Major Projects and Urban Syste
2 . Department
Figures in brackets indicate the literature references at the end of this paper.
213
engineer sizes and selects the equipment he intends using in part three. Part three is the systems
operation simulation. It simulates the performance of the system selected in part two. The simulation
takes into account such items as equipment performance curves at partial loads, control set points,
lighting system interface with the space conditioning system, etc. Various systems may be inserted in
part two and their operation simulated in part three. The final print out of all three sections is,
hourly electrical requirements, hourly fuel requirements, maximum percent heating plant load, maximum
monthly fuel use, and monthly maximum electric demand.
For large buildings the accuracy of this type of program is necessary. However, for small com-
mercial buildings this type of program is not normally used.
In this study the results of a smaller, less sophisticated program were compared to the West-
inghouse program. This program is a computerized manual calculation which took approximately 540 man-
hours to develop. The program was designed to analyze the small commercial buildings which were being
done manually. The program uses the ASHRAE method of load calculation and combines this with a mod-
ified degree day approach to arrive at the estimated heating energy consumptions. The air condition-
ing energy consumption is based on equivalent full load hours for the equipment.
The final print out of the Duquesne Light Company program gives the design heating capacity for
each zone, the estimated air conditioning capacity at two hour intervals from 8:00 a.m. to 8:00 p.m.,
the monthly electrical requirements and associated costs based on Duquesne Light Company's rates for
all the electrical usages in the building.
2. Description of Input
For the same building, the Westinghouse program has about 40 sheets of input data with approxi-
mately 1,000 pieces of input information. It takes about 12 man-hours to fill out the input sheets.
On the other hand, the Duquesne Light Company program only has 3 pages of input sheets per zone (max-
imum of nine zones) with approximately 500 pieces of input information. It requires up to 8 man-
hours to fill out all of the sheets.
3. Description of Cases Studied
In order for a valid comparison to be made, three buildings were used in the comparison. The same
input data was supplied to both programs. The first building studied was a 10 story office building
with about 60,000 square feet. The second building was also an office building. This building had a
floor area of approximately 300,000 square feet. The third building was a large two, and in some
places, three story structure, with over 700,000 square feet of floor area.
No energy consumption data was available for building number one. The second building was opera-
ted on an 8 to 10 hour per day schedule. The third building was occupied 24 hours per day, except for
a small portion of it which was used as offices.
The buildings are larger than what the short form program was designed to handle. However, these
three buildings were the only ones available for comparison.
Since the Westinghouse program has the capacilities of performing hourly calculations, building
operation simulation was straight forward. However, judgment had to be used when using the Duquesne
Light Company program, since it simulates the operation as either day or night operation, and average
conditions must be assumed.
The accuracy of the Westinghouse program has been established in several comparisons apart from
this paper. In one case where actual weather data and building characteristics were put into the
computer after the building had been in operation for a year, the computer was within 0.3% (three-
tenths of one percent) of the actual consumption. In other studies similar results were obtained.
Therefore, for the purposes of this paper, the short form program was compared to the Westinghouse
program.
4. Results
Tables 1, 2, 3 and 4 show the results of the short form program as compared to the Westinghouse
program.
214
Table 1. Comparison of short form capacities to the Westinghouse heating and cooling capacities
for building number 1.
Heating Cooling
Duquesne Light % Duquesne Light %
Westinghouse Company Difference Westinghouse Company Difference
1.
44,425
42,763
-3.9
112,191
120,390
7.3
2 .
102, 807
98, 240
-4.4
184,552
157,726
-14.5
3.
44,425
42,763
-3.7
100,204
100,429
0.2
4.
137,573
131,340
-4.5
204,214
175,473
-14.1
5.
1,394,776
1,311,305
-6.0
2,366,416
2,245,000
- 5.1
6.
205,137
199,605
-2.7
309, 110
296,203
- 4.2
7.
8.
9.
1,354,725*
1,264,409*
-6.7
1,077,100
802,800
-25.4
Total
3,283,868
3,090,425
-5.9%
3,927,000
3,812,000
-2.9
Ventilation load of building
Table 2. Comparison of short form capacities to the Westinghouse heating and cooling capacities
for building number 2.
Heating
Cooling
Westinghouse
Duquesne Light
Westinghouse
Duquesne Light
Company BTUH
Deviation
BTUH
Company BTUH
Deviation
1.
1,079,488
1,068,852
-1 %
1,069,377
1,328,687
+24 %
2.
498,806
336,823
-32 %
562,590
894,505
+59 %
3.
1,194,213
1,178,269
+ 1.3%
1,228,649
1,890,470
+ 55 %
4.
402,907
369,908
+ 8.2%
491,790
534,139
+ 8.5%
5.
1,413,635
1,119,166
-21 %
1,923,085
2,123,450
+10.5%
6.
65,801
693,781
+ 11 %
686,005
477,152
-30 %
7.
528,107
567,818
+ 7.5%
573,527
870,900
+52 %
8.
206,400
256,383
+ 24 %
264,581
289,649
+ 9.4%
9.
3,020,613
3,203,347
+ 6 %
4,045,156
4,781,861
+18.3%
Total
9,701,524
8,794,347
-9.4%
11,257,705
11,820,000
+ 5 %
Table 3. For building number 3.
Heating
Cooling
Westinghouse
Duquesne Light
Westinghouse
Duquesne Light
0,
B.T.U.
Company B.T.U.
Deviation
Tons
Company Tons
Deviation
1.
2,116,178
2,267,999
+ 7.2%
365
376
+ 3 %
2.
6,164,014
6,559,231
+ 6.4%
823
845
+ 2.7%
3.
2,507,617
2,724,041
+ 8.6%
172
187
+ 8.8%
4.
3,246,680
3,484,565
+ 7.3%
237
246
+ 3.8%
5.
2,925,500
3,074,979
+ 5.1%
332
344
+ 3.6%
6.
3,547,782
3,731,313
+ 5.1%
336
360
+ 7.1%
7.
795,753
940,095
+ 18 %
36
42
+16.5%
Total
21,303,500
22,782,176
+ 7 %
2,301
2,362
+ 2.6%
Table 4. Compari
sons of annual
consumptions .
HEATING
COOLING
TOTAL
Duquesne
Duquesne
Duquesne
Westinghouse Light Co. Westinghouse Light Co. Westinghouse Light Co. Difference
9,598,000 1,912,000 2,507,000 11,593,000 41,725,000 47,675,000 +14 %
6,920,000 3,155,000 2,386,000 3,185,000 22,449,000 19,064,000 -12.5%
Bldg. 2
Bldg. 3
215
For large complex buildings with complicated environmental systems it is felt that the accurate
results obtained from the Westinghouse program make it far superior.
The comparative tests show that for capacity comparisons the short form program is fairly accurate
for total building capacity. The biggest difference of the three test cases was only -9.4% and the
smallest +2.6%. This comparison did point out, however, that on certain zones, due to their orienta-
tion, the short form program can be as much as 59% high on cooling. This value, one for 55% and one
that is 51% high are shown on table 2. These errors resulted from all of these zones peaking early in
the morning. The short form program assumed maximum temperature differential at this time. Due to the
ability of the Westinghouse program to look at each hour of the year, it was able to determine more
accurately the number of people in the zone and the ventilation for that hour. The Duquesne Light
Company short form program has only the ability to decide between day occupancy and its ventilation
rate or night occupancy and its ventilation rate.
The results of the annual energy consumption were much different. Although the total consumption
was 12.5% low for building number two and 14.0% high for building number three, the Kwh usages for the
various components were way out of line. The heating consumption was estimated as much as 90% low.
The cooling consumption was as much as 300% high (see table 4).
These large errors are due to the equations used for estimating the energy consumption which are:
Annual Heating Consumption
,, , (Heat loss day - Internal load day) Degree day at change % day ,
Day Kwh = ^r^cZ 7-- — 1 z — t. ■ i x* ^ ■' ^ x ^■:x24 hours per day
Temperature differential at which over temperature operation ^
heat loss was calculated
Ni ht Kwh - (Heat loss night - Internal load night) ^ Degree days at night % night 24 hours
Temperature differential at which temperature operation ^ per day
heat loss was calculated
Annual Cooling Consumption
Cooling Kwh = Tons cooling x Kwh/ton x Effective full load hours**
24 X D X C
**Effective full load hours = — -t —
tm - td
D = Cooling degree days on base temperature equal to change over temperature
^ J ■ ^ ^ Daily Range,
tm = (outdoor design temperature - ^ ^)
td = change over temperature
c = % time space is air conditioned
The above equations do not adequately handle the large internal zones of major buildings with
their high internal heat gains, and the short form method appears to work best in smaller exterior zones
having more standard heating requirements.
The hourly analysis is far more accurate in estimating annual consumption for large complicated
buildings than these empirical formulas. These formulas were developed from test data obtained from
samplings of offices and commercial buildings located in large metropolitan areas. For small offices
and commercial buildings these approximations are reasonable. For the larger building with large
interior zones, known also as core areas, these formulas do not yield accurate estimates.
5. Conclusions
This study shows that for estimates of heating and cooling, the short form, when used with judg-
ment, can be fairly accurate.
However, this study pointed out that for an annual estimate of energy consumption, a program that i
analyzes the building systems hourly is far more accurate than one using the old empirical equations.
This becomes even more important on very large buildings with many large internal zones.
6. References
[1] American Society of Heating, Refrigerating and Air-Conditioning Engineers, New York, ().
216
Energy Estimating - How Accurate ?
Robert Romancheck, P.E.
Pennsylvania Power & Light Compajny
Allentown, Pennsylvania
The Heating and Air Conditioning Engineer has , during the past five years ,
endeavored to utilize the vast capabilities of the computer to synthesize highly
sophisticated mathematical models for use in problem- solving. This paper is an
attempt to relate (1) How we designed a building load and energy estimating com-
puter program and (2) Propose the hypothesis that greater programming sophis-
tication does not necessarily mean better estimating of energy consumption.
Work to computerize heating load and energy calculations was initiated in
196h and the implementation of computer studies began in - The complete
system as it has evolved to date includes five programs:
1. A sort routine.
2. A design heat load and an energy estimate based on degree day data.
3. A design cooling load with an hourly synthesis of the projected
thermal requirements integrated with U. S. Weather Bureau Data.
h. Hoinr-ly energy summation routine
5. An on-site generation, total energy analysis, hourly computation.
Engineering studies relating to energy costs are usually undertaken in
order to determine the most economical fuel to use. Many computer programs
have been written and will be written in an attempt to make this complex
task easier. We often wonder where does one choose to end their program
development and what "K" factor is used to account for this decision.
Key Words: Air conditioning, computer methodology, computer program
evaluation, energy determination, heat loss, heat pumps, solar effect.
Weather Bureau data.
1. Introduction
The ability to predict, within predetermined accuracy limits, design loads and energy consumption
of a building's environmental system can now be reliably accomplished on a dynamic, rather than static
basis, through the use of computers. Complexities of conditioning systems, capital costs and the com-
petitiveness of energy suppliers have become so interrelated that the designer must now have this capa-
bility. At the same time, however, computer routines must be realistic in the amount of input data
required and the relative accuracy of the results generated. The computer programs that are discussed
here are written in both Fortran II and PL/1 programming languages, and are operational on IBM 707^,
lOK storage, or an IBM 360 , Model 60 525K storage computer.
2. Program Methodology
2.1 Philosophy
In 196k studies were undertaken to determine the feasibility of using an IBM 707^ computer to pro-
vide estimates of energy needs for space heating installations. This was necessitated because engi-
neers in the sales group were spending most of their time preparing owning and operating cost analyses .
This severely limited their ability to penetrate the bulk of the space heating market which, in turn,
led to our basic philosophy with respect to this computer application — development of a routine that
didn't need an engineer to supply the input data, but which would still yield results that were more
accurate than any method available. This concept would allow preparation of the greatest number of
operating cost studies, thereby effecting maximum market penetration.
217
The initial reasoning was to write a computer program capable of integrating "building heat losses
and gains, and heating and cooling energy requirements. This idea was soon discarded because of the com-
plex logic and the time delay required for debugging a program of this magnitude. A sequential program
system was then investigated and subsequently proved to be the best solution to our problem. In selecting
this method the first program would be written to generate design load calculations and energy use by the
degree day method. Calculations from this program could then be stored on a tape file for use as input
data in subsequent routines. It is believed that program debugging was considerably reduced by this
sequential system. It was also determined that routines must be compatible for residential, commercial,
and industrial estimating use.
2.2 Heating Program
Program #1, Design Heat Loss Determination, has as input the various building design characteristics
such as :
1.
Wall, roof and floor constructions
2.
Window and door constructions
3.
Building orientation
k.
Design temperatures
5.
Wall, roof and floor areas by zone
6.
Internal heat gains
7.
Ventilation rates
8.
Occupancy schedules
Figure 1 illustrates the input data form used for this routine. All heat losses are calciilated by
zone, according to the methods outlined in the "ASHRAE Guide." Internal heat gains are also calculated
for both the occupied and unoccupied periods and are used to adjust the building heating load require-
ments. Cooling load determination was not part of the original operating system design. The occupancy
schedule input sheet, figure 2, can be as complex or as simple as the application requires. A file of
resistance values for the more common building materials is also on call. Simply by inputting a 3 digit
number and the material thickness, coefficients of transmission (U values) can be generated. The user
also has the option of developing his own "R" or "U" value and inputting this number on the data sheet.
Building ventilation needs can be determined by one of three methods, number of air changes, cfm per
occupant or infiltration by zone. Infiltration values are based on the most representative data cur-
rently available. It is a personal observation that additional work needs to be done in the area of
infiltration rates based on varying wind speeds and the newer types of windows and doors currently used
in construction. One other element of Program #1 is the calculation of an energy requirement based on
the degree-day method. Initially, this was the quickest way to get our system operational and since
studies were at that time calculated by using degree days, accuracy could only improve. The use of this
routine was placed into production in the spring of . Computer outputs (fig. 3 and 'k) were generated
for residential, commercial and industrial installations at the rate of 20-30 per day.
2.3 Air conditioning program
Program #2, Air Conditioning Load Determination, was designed to complement the first routine by
providing cooling load information. Calculated values from Program #1 were written on a tape file for
use in this program and without any additional input, air conditioning design loads were provided. This
was an interim procedure, however, since the programming efforts to provide this information was minimal
compared to hourly energy requirement determination.
In order to provide the optimum result it was of course necessary to integrate weather data into
the system to obtain a reliable synethesis or projected hourly thermal requirements. We had at our
disposal 5 years of data from the U. S. Weather Bureau. An attempt was made at averaging the data
(discarded this method because of the loss of temperature extremes) or creating a typical year (dis-
carded becaiise of definition, what is "typical"). The final decision was to use the year that was most
in line with the normal n\mber of degree days for the area. The hourly observations used, temperature,
specific humidity (obtained by calculation from the dew point temperature) and cloud cover (50^ cloud
cover or less constituting a sunny hour), were recorded on a tape file. Because of computer core
limitations of the lOlh computer, it was necessary to average two hours of observations into one hour.
This use of weather data will probably prove interesting and hopefully will provoke some deep
thought and your consideration. First, each building zone is analyzed hourly, to determine whether
it requires heating or cooling. Solar load is an important consideration at tliis point. If the sun
is shining, (50^ or less cloud cover) a calculation of the solar effect is made. The design solar
load, as calculated by the sol-air temperature difference method developed by Messrs. C. 0. Mackey and
L. T. Wright, Jr. with additional work by Mr. J. P. Stewart, is used to predict the hourly BTU gain on
the various building zones. The energy gain is then calculated to equal, the design solar load multi-
plied by the ratio of the temperature occurring at that hour, divided by the cooling design temperature.
218
Solar Heat Gain (BTU's) = Design Solar Load x Amjlent Temperature
Cooling Design Outdoor Temperature
This solar effect is applied to the building energy needs in the heating as well as cooling season.
Since input energy to a refrigeration machine varies with load, outdoor temperature, design of con-
ditioning system and majiuf acturer , some assumptions had to be made with respect to equipment energy use.
Our entire problem-solving system, as we previously mentioned, is based on a production basis philosophy
It was therefore necessary to provide an equation, obtained from a regression analysis, to recognize the
different characteristics of various manufacturers' equipment. This does not preclude the ability to
input a curve based on a specific piece of equipment and generate results relative to its use. An
output was then generated (fig. 5) which contained summations of hourly heating and cooling energy re-
qmrements. Additional information was included in the output as an aid to the system designer.
2.k Heat Pump Option
Since the determination of a heat pump Coefficient of Performance (CO. P.) is obtainable only by
an hourly analysis, the routine posseses this facility also. We do not compute heat pump feasibility
studies on a production basis, but rather on an individual need, using a specific manufacturer's input-
output energy relationships .
Residential dwelling unit studies are not included in the hourly energy analysis. Much time and
effort was spent in trying to correlate known operating energy usage with the hourly routine projection.
Constant internal heat gains, variable gains, various occupancy schedules, set back temperature con-
ditions were all tried without success. The EEMA equation, in our estimation, still yields the best
solution of heating energy determination for residential units.
2.5 Total Energy Routine
Since we are constantly developing and overlaying hourly BTU building thermal needs, it is a
relatively simple procedure to create a file storing these values and use them as input to a so called,
"Total Energy," isolated generation routine. The BTU values are initiaiized positive, if heating, and
negative, if cooling, for identification purposes, before being placed on this file.
Additional input required for this run consists of the specified engine or turbine fuel rate
c\irve, waste heat availability curve, hourly electrical demands (weekly, monthly, etc.) and hourly pro-
cess steam loads, if any. This data is then merged on an hourly basis with the building thermal re-
quirement and an output generated (fig. 6) which lists hourly KWH generated, cooling or heating BTU
requirements, process heating BTU requirements, if any, and ciibic feet of gas or gallons of oil re-
quired. A summary is also developed which includes annual KOT, gas or oil needs and an overall thermal
efficiency of the isolated generation system. The hourly output is generated in order that any
doubter would have the ability to verify the calculated quantities.
3. Program Evaluation
3.1 Industry Interest
The accuracy of these programming routines , we believe , has been demonstrated not only by actual
billing records, but also by the acceptance of electric heating in the residential, commercial and in-
dustrial markets. The present total-electric customer breakdown within our Company area includes
jit.OOO residential units, k,000 commercial units and 2h0 industrial installations out of a total of
820,000 billed accounts.
There are numerous organizations that have heating and cooling design and energy calculation com-
puter programs available and in use. Some of these include: The Electric Heating Association, ^
American Electric Power, Westinghouse , American Gas Association, Automatic Procedures for Engineering
Consultaats (APEC) , Post Office Department (TACS) and numerous consultants and utilities . The degree
of complexity varies widely and in all probability the results also. This leads into the next dis-
cussion.
3.2 The Unknown Factors
a
In after making a presentation to an ASHRAE Task Group on the procedures we had m use , _
letter was received which in part stated, "the Task Group is attempting to develop a veiy sophisticated
calculation program that will take into account all significant factors affecting the heating and
219
cooling loads." The initial reaction to this statement was to recall oior own experience when we began
to define and analyze the many variahles in this problem. Which of these variables do you choose to
exclude and which do you include and a directly related question, how long will it take to provide the
input data and obtain the results?
Who will decide what is significant and what isn't? Where will new data be supplied for infiltra-
tion values or isn't it significant? U. S. Weather Bureau data is recorded at the airport. Must all
new buildings be built on a runway for the data to be applicable or isn't this significant. Some
weather data, such as cloud cover, are only observations. What factors do we use to account for this?
In the preliminary design state of a mechanical system all components, ducts, etc. must be engineered
for the various systems in order to be able to select the best. Who will do this or "Isn't it signifi-
cant?" Contractors build structures in varying degrees of soundness. What "K" factor is used to
adjust the estimate, particularly since we don't even know who the low bidder will be. Building
occupancy schedules in actual operation rarely, if ever, agree with the preliminary objectives. How
do we adjust the energy estimate. Do we continually adjust the resistance values of building materials
relative to outdoor temperatures or do we neglect this? How do we compensate for thermostat settings
ranging from 69°F to 78°F or isn't this Important? Control systems must be designed to properly
monitor the system. But control system contracts are given to the low bidder as are most other con-
tracts, what's the "K" factor relationship here?
The basic problem being introduced should be obvious. What real value is there in computing the
sun's exact angle relative to a new building when someone comes along and builds a structure adjacent
to it. The building unit is a dynamic living entity not a static dormant box. The complexities of any
program input must be justified by the accuracy of the program output. It is also the moral obligation
of the industry to honestly evaluate all , not just some, building energy needs, whether the structure
contains 200 square feet or 2,000,000 square feet. It is seriously doubted that these evaluations can
be made for all clients unless the cost and program input are reasonable.
3.3 A Comparison
We recently compared the results of a study with one of those complex routines, which hourly com-
putes the solar altitude, azimuth and incidence angles, and requires a various assortment of other input
data. In no case did a zone heat loss, heat gain, heating or cooling energy requirement vary by more
than 5/? and in most cases, the difference was negligible.
Energy analyses are necessary in the preliminary planning stages with preliminary design data
since this is when decisions are made. Deeper analyses of systems and designs are necessary, and
should be done on operating systems, in order to determine what is the optimum system design. ^ The^
ability of computer programs to generate reliable and accurate results by using complex relationships
with numerous unknown inputs must at least be questioned.
220
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207 PUster, Sam) Aftg.
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137 SUdl(i« Door
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141 Slldina Door
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143 RfildrncUl
143 CunnwfcUl
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163 SwlQgLng 10
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221
IDf Mill >CKtt01t
ELECTRIC SPACE. HERTING ESTIMMe
1 f
HOUBS OF MRMALOiE
;
1
"
P
i
OF Uat
THU
FKI
SUM
RtWARR^ & NOTES
t
C
II
6
F
ennsvlv6n(4 power c light company
[electric space heating estimate
PPf.L PIST. I
ESTIMATOR JKS
OFFICE BUILPING
BETHLEHEH PA
NORMAL DEGREE DAYS 5-lCO
RATF HS
OATf TF SURVEY l2/l2/l-<)
CONSTRUCTION PES.
GROUND FLOOR A - FLOOR 3EL0H GRI) 34,00
EXTERIOR WALL B - U VAUIF CE INSULATION .lOCO
ROOF C - U VALliE HF INSULSTION .10^0
WALL BELOW GRO 0 - BELCw r.RAOE
OLSKN Tfso.
IN -ISf StT8M,»;
INT IXI INT iXT
WINDOWS c nriiRS pts. infil.
A - PICTURE GLASS VFRT. 0.99 1.2^
B - COM" nOOR GLASS VFRT. O.H? b.C:
SCHfcOULE OF USE WEEKS ''0^ TUf WED THU FP I SAT SUN
i. A 0 5? 7 2C 7 ?0 7 20 7 2C 7 20 3 13 0 0
Figure 3
222
•eNN'iYiviNio POMFR c trr.HT cn.
fLECTOIC SPACE ffATING ESTIMATE
IBM OFFICE BUlLDINr,
BETHCEHE'' PA
OUTSIDE
AREA EXPOSURE OIHENSirNS TYPE
FIRST FCR
HALL
UALL
FinnH
WIN»nw/DR,
1 1 Norw/nR.
KlNnrw/DR.
KiNOrw/OR.
ul NUnu/OR.
ulNCnu/OR.
u I Monj/nR .
H INDOW/nP .
HiNnnu/nR.
■iNLPw/nR.
rtlNnOri/OR.
I NF IL IR AT ION
V F N T 1 1 A T I ON
rCCUPANCY
( ir.HT ING
OTHER r.AINS
536.
536.
168.
1 W,
!<)(■•;
I 71 '.
St:65
-
-?a66S
S
HEAT RfO.
I M WATTS
0
SUB-TOTAL
J
StCON'l FtP KAIL
37 HINOOW/OR.
1 wiNnow/riR.
P WINOCW/PR.
1 UINDOU/DR.
2 wINOnw/np.
-^3 >iiNonw/nfl.
26 WINOrw/OR.
26 «iNnnH/nR.
INF IL IRAt ION
VfNI IIAI ION
I Cf UPANCY
L irn ING
TTHER GAINS
536. C K 12.0
2.0
3.0
<..r
3 "! M 3 9
1 1 >> 1
'.772
1 193
^
35'i5^t
35^.54
i Ibl 2
-2^1 OC
3 1 H I
35 79
5M536
:'
'5',5<.
SU3- TOTAL
2 74 320
a WALL 5
'♦3 WINOOH/nR.
'.3 VJINDCW/OR.
26 WINOCW/OR.
26 HINCOW/OR.
INF IL TRAT ION
VENI 11 AT ION
OCCUPANCY
L IGHTING
OTHER GAINS
5 363 6
(1
-200O0
-2 )64C6
35 ,54
I2 90C
2 32 761
FOORTH FLR WALL
OVERHE AC
4J hINUCh/DR.
43 VIINnOW/nR.
25 MlNDCW/OR.
25 vrlNOOw/OP.
I NF IL TRAT ION
VENTILATION
OCCUPANCY
L ICHTING
OTHER GAINS
536.
16fl.
3
1
1 54 5 4
3 5 4 5 4
12 9CO
2
-'OCCO
-2 )64C6
1 290C
0
SUB-TOTAL
ESIIMATEC ANNUAL KyH
eSTIMATEC ANNUAL COST FOR HEATING
TOTAL NET HALL AREA
SQUARE FFFT.
TUTAL FLOOR AREA IS 672CC SQUARE FEET.
COST PER SaUARE FOOT IS S 0.13
TOTAl VOLUME IS CUBIC FEET.
COST PES HUNDRED CUBIC FEET IS I 1.12
NOTE. THE HEAT LOSS CALCULATIONS AND EST!"AIF OF OPERATING CISTS
IN THIS PROPOSAL ARE flASEO ON ACCEPTED PPACIICtS OF THE
HEATING INDUSTRY. THEV APE OETrRMINFC ON THE BASIS OF
NORMAL CONCITICNS WITH NO ALLOWANCE FOR UNUSUAL WEATHER
CUNDITICNS OR VARIATIONS IN INDIVIDUAL LIVING HArtlTS,
SUCH AS MAINTAINING UNUSUALLY HIGH TFMPERATUkES OR
EXCESSIVE VENTILATION. IT 15 RtCUXMENOELl THAI THE
INSTALLED WATTS RE INCRFASEE IN CAPACITY WHENEVER
lEHPEPATURE SETBACK IS PLANNED.
Figure 4
223
PENNSYLV4NIA POWER UNO LIGHT COMPANY PPCL DIST. I
ESIIMATOB JKS
HOURIY HEATING E COOLING ENERGY ESTI'57
HEATING BTU
FOURTH FLR
HOURS IN USE
36'. 0
CHANGEOVER TF-PEPATURE
5B
WALL BTU GAIN
76C3
ROOF BTU GAIN
a90'tf'
WINDOW/DOOR BTU GAIN
225
s ;
BASIC
ROOM
DATA
SPECIAL
INTERNAL LOAD
DATA
3
ROOM
1 0.
AZIMUTH
+ WEST
LENGTH
OF
EXPOSURE
(FT )
WALLS
WINDOWS
DOORS
EXTERNAL SHADE
A
B
a
A HOUR
8 HOUR
3
;5
t
EXPOSURE DATA
NOTE: HEAVY VERTICAL LINE INDICATES DECIMAL LOCATION
ROOM DATA
Figure 1. Room Data
253
MARGIN FOR TOP BINDING
o
ROMINE & SLAUGHTER. INC. ♦» CONSULTING ENGINEERS FORT WORTH, TEXAS
JOe 565/e NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 »* PAGE 1
GENERAL BUILDING DESIGN DATA
««»»♦■»««♦«»«»*«■»«««#«■»*♦«»»«
HOURS TO BE CHECKED FOR PEAK COOLING LOAD
9 10 11 12 13 14 15 16 17 18 19
HEAT ING
MONTH OUTSIDE
(SUN DB HUMID.
LOAD) TEMP. RATIO-
1 10.0 0.
INSIDE
DB HUMID.
TEMP. RAT 10-
75.0 0.
COOLING
MONTH OUTSIDE
OF DB HUMID.
CALC. ThMP. RATIO-
8 100. U 0.
INSIDE
DB HUMID.
TEMP. RATIO-
78.0 0.
MASTER CONSTRUCTION FACTORS
HOUR ROTATE BLDG. OFF SOUTH. WALL
AVG. DEGREES (EAST-. WEST+) HT.
5 -19.0 9.0
(NOTE — HTG. CALC. MADE FOR LISTED DATA )
(ONLY. COOLING CALC. MADE FOR EACH HOUR I
(IN CALC. MONTH (OUTSIDE DATA INPUT ARE )
(UPPER LIMITS OF DAILY WEATHER CURVES). )
o
MASTER INTERNAL LOAD DATA
**-ft*******it*************»
OCCUPANCY
BTU/PERSON — HOURS IN- SF PER
SENS. LATENT FROM THRU PERSON
220. 230. 9 17 100.
LIGHTING
WATTS PERCENT-
/SF — TO RET.
5.0 60.
AIR
INFILTRATION
CHANGES MULT. FACTOR
PER HR. FOR BLDG TOTAL
0.0 1.00
VENT ILATION
CHANGES CFM PER CFM PER MAX SF PER
PER HR. SF PERSON- PERSON
2.0 C.25 25.0 125.
BUILDING LOAD DIVERSITY FACTORS
MAX. PEOPLE MULTIPLIERS. TIMES SUM
IN BLDG. OF ZONE TOTALS
(OVER-RIDE) LIGHTS PEOPLE APPL.
90. 0.90 1.00 0.75
DEHUMID
TEMP RISE.
DEGREES
22.5
SYSTEM TYPE-
0 = D.X.
1 = CH. WTR.
(NOTE — ALL MASTER INTERNAL LOAD FACTORS. PLUS HOUR AVERAGE AND WALL HEIGHT )
(FACTORS. MAY BE OVER-RIDDEN BY SPECIAL DATA INPUT ELSEWHERE. IF NO SPECIAL)
(INPUT. THESE FACTORS WILL BE USED. DIVERSITY FACTORS ARE OPTIONAL. )
MARGIN FOR STANDARD 3-HOLE BINDING
o
8 '/2"
c
^STANDARD SHEET SIZE
Figure 2. Typical Printout - Master Data
254
ROMINE
& SLAUGHTER* INC.
*# CONSULTING ENGINEERS FORT WORTH* TEXAS
(^JOB 56b/B NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 »*
PAGE 2
WALLS
## * # #
TYPE
GENERAL
DECREMENT
TIME WALL- U FACTORS
OL. " U r\ C
NO.-
DESCRIPTION
FACTOR
LAG- COLOR WINTER SUMMER
6TUH/SF~
1
4. BRICK, 8. TILE
0.39
5. D 0.33 0.31
0.0
2
LIKE 1 + PLASTER
0.39
6. D 0.29 0.28
0,0
3
12.C0NC. TO GRND
0.00
0. M 0.00 0.00
2,0
ROOFS
««•««»
TYPE
GENERAL
NO.-
DESCRIPTION
FACTOR
LAG- COLOR WINTER SUMMER
1
2. CONC. 2. INS.
0.69
5. D 0.12 0.11
2
LIKE 1 W/ CEILG.
0 • 6 9
a r\ r\ ^ r\ nno
0 • u u»iu u»uy
PARTITIONS
»»««#»#»♦*
TYPE
GENERAL
U r-ACTOKS
UNCuInD* AKcA ItMr*
NO.-
DESCRIPTION
BTU/HR/SF
WINTER — SUMMER —
1
4. TILE TO STOR.
0.40
40 • 90 •
FLOORS
♦»♦*»«
FLR.
GENERAL
U FACTORSf
UNCONDlTIOiMEO SLAB LOSS
FLR» CLG
TYPE
DESCRIPTION
DlU/nK/or—
AKtM It. nr. DLW oK UN oK —
0NLY=1 ,
NO.-
OF FLOOR
WNTR sumr
WNTR. SUMH. BTU/SF BTU/LF
B0TH»2 —
1
4. CONC. » INS. .CLG
0.08 0.08
10. U. 0.0 0.0
0
2
4. CONC, CLG.
0.27 0.22
40. 90. 0.0 0.0
2
3
4. CONC. TO BSMT.
0.44 0.60
60. 83. 0.0 0.0
1
SLAB ON GRADE
O.UO O.UO
0. U. 0.0 42.0
0
5
SLAB BLW. GRADE
O.UO 0.00
0. U. 1,0 0.0
0
6
4. CONC. TO STOR.
0.44 0.60
60. 9U. 0.0 0,0
1
NOTE — ZERO OR BLANK INPUT
FOR WINTER
OR SUMMER TEMPERATURE
WILL BE
CALCULATED AS OUTSIDE DESIGN
n D V Q 1 1 1 Q
o
Figure 5. Typical Printout - Master Building Shell Data
255
o
ROMINE 6 SLAUGHTER* INC. »♦ CONSULTING ENGINEERS FORT WORTH. TEXAS
JOB 565/B NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 «* PAGE 7
ZONE DIVERSITY DATA
»»»«««»-»«»»♦**«<■♦«»
ZONE ZONE NAME-
MULTIPLIERS. TIMES SUM VENTILATION FACTORS-
NO.-
OF ROOM
TOTALS-
CH6S
CFM
CFM-
FIXED ALL-
DESCRI PT ION
LIGHTS
PEOPLE
APPLI .
/HR.
/SF
/PER
VENT-CFM O.A.
ENGINEERING AREA
1.00
0.90
1 .00
2.0
0.25
30.0
REPRO. 6 MAILING
1.00
1.00
0.75
2.0
0.25
25.0
X
PERSONNEL MNGMNT
0.95
1.00
1.00
2.0
0.25
25.0
0.
^000
SERVICE & STORES
l.OU
1.00
1.00
2.0
0.25
25.0
EXECUTIVE SUITE
0.85
1.00
1.00
2.0
0.25
25.0
.
DISTRIBUTION
1.00
0.80
1.00
2.5
0.30
25.0
ZONE
MAX I MUM
ZONE
INSIDE
DESIGN
COND. —
ZONE
AIR SYSTEM
MISCELLANEOUS-
NO.-
PEOPLE-
WINTER —
SUMMER
DTR-
0=RM UNIT.
OMIT
PERCT
IN
TEMP
HUMI D.
TEMP
HUMID.
DEG.
1=L0W PR..
CALC. —
SAFT.
ZONE
DEG.
RAT 10-
DEG.
RATIO-
F.—
2=HIGH PR.
HTG CLG
FACT.
35.
75.
0.
75.
0.
22.5
1
10.0
5.
75.
0 .
78.
0.
25.0
1
0.0
«•
75.
0.
78.
0.
22.5
0
X
0.0
«.
60.
0.
78.
0.
22.5
0
X
0.0
60.
77.
0.
72.
0.
22.5
2
15.0
18.
75.
0.
78.
0.
22.5
2
0.0
(NOTE — ALL ZONE DIVERSITY DATA IS OPTIONAL INPUT. TO OVER-RIDE BUILDING MASTER )
(DATA. AIR SYSTEM TYPE SHOULD ALWAYS BE SPECIFIED. TO ACCOUNT FOR APPROPRIATE )
(AMOUNT OF FAN HEAT. DUCT GAIN. + DUCT LEAKAGE — 0 FOR ROOM FAN AND COIL UNIT.)
(4 PERCENT FOR LOW PRESSURE DUCT SYSTEM. AND 12 PERCENT FOR HIGH PRESSURE DUCT )
(SYSTEM. ADDED TO ROOM SENSIBLE LOADS. SAFETY FACTOR IS A PERCENT FIGURE TO BE)
(ADDED TO ROOM SENSIBLE. LATENT. AND HEATING LOADS. ♦ = SUM OF ROOM TOTALS. )
(MASTER DATA LISTED IF NO OVER-RIDE INPUT. )
o
Figure 4. Typical Printout - Zone Diversity Data
256
■JOB NO.
■FIRM NAME
CALCULATION DATE
PROJECT TITLE
CALCULATION
PAGE NO;
R-QMINE £r SLAUGHTERt INC. »* COiNSULTIiMG ENGINEERS / \ FORT WORTH. TEXAS
NBS/ASHRAE/APEC SYMPOSIUM ♦ SAMPLE PKOBLEX 11/30/70 *♦ PAGE 16
JOB 565/8
ROOK 201
PRINT ROOM
DIMENSIONS
LENGTH WIDTH HEIGHT
16.00 12.00 10.00
ROOF-
AREA TYPE
192.00 1
AREA
192.00
FLOOR-
TYPE
4
AREA
192.00
PARTI TIGN
TYPE AREA
1 UO.OO
CFM
INPUT MIN
INFL EXH. A/C
0 30.0
PEOPLE
IN HOURS- BTU/HR EA.
RM IN OUT SENS LAT
2 9 17 220. 280.
LIGHTING
WATTS
TOTAL W/SF
960. 5.0
HOURS- PCT TO I^INCAND
ON OFF RETURN 0=FLUOR
9 17 0.0 0
APPLIANCES
HOURS- SENSIBLE HT
PERCENT TO-
LATENT HT PERCENT TO-
HOUR
AVG.
ON OFF
BTU/HR
ROOM- RAD.
BTU/HR
ROOM-
RAD.
USED
9 17
.0
70.0 30.0
.
100.0
0,0
3
EXPOSED
AZIMUTH
ANGLE
EXPOSD
WALL A
WALL B
WNDiv A
WNDW a
DOORS-
INPUT-
ACTUAL
LENGTH
TP AREA
TP AREA
TP NO
TP NO
TP NU
180.0
161 .0
16.00
1 119.00
0 0.00
3 1
0 0
2 1
90.0
71.0
12.00
1 120. UO
C 0.00
0 0
0 0
0 0
(NOTE - TIME
(FIGURES ARE
( INCLUSIVE
EXT. SHADE-
FR TO FR TO
0 0 0 0
0 0 0 0
o
peak; LOAD DATA FOR ROOM 201. OCCURRING AT HOUR NO. 17-
HEAT GAIN —
SENSIBLE
WINDOW
.
WALL
.
ROOF
..
PARTITION
384.
FLOOR
0.
DOOR
216.
-INF ILTRATION
0.
LIGHTS
.
PEOPLE
439.
APPLIANCES
.
FAN HP(0.04)
678.
SFTY FAC(O.OO)
0.
SUB-TOTALS
.
TOTAL HEAT
.
DEHUMID TEMP RISE
25.
RM CFM = 653. 7»
650.
««»»»
- HEATING
INT. GAIN
.{ B.TU./HR. )
CHECK FIGURES
( TOTAL HEAT 1
COOLING
115.7 BTU/SF
11.6 BTU/CF
103.7 SF/TO-\
HEATING
57.6 BTU/SF
5.8 6TU/CF
17.4 SF/M6H
0.
.
.
.
-. LOSS LESS INTERNAL GAIN
415. WINDOW SOLAR GAI>N
-. NET LOSS — LESS INT. + SOLAR
««»»» FOR 3.0 MINUTES/AIR CHANGE. AND 3.4 CFM/SF
O
ZONE
ROOM 201 PRINT ROOM
<
I-
<
Q
O
O
<
I-
<
Q.
I-
Z)
>°
<
o
o
o
ir
Figure 5, Typical Room Load Printout
257
o
JOe 565/B NBS/ASHRAE/APEC SYMPOSIUM « SAMPLE PROBLEM
11/30/70 ♦* PAGE 17
LISTING OF ZONES IN WHICH
ROOM 201 APPEA
-fi- * -& * ^t * <^ »t * * * J> -i.- * *- -R-
kS (MASTER OK
DUPLICATE). AND
HOW OFTEN
ZONE ROOMS
1
HOURLY COOLING LOADS. ROOM 201
;: * « •»
PRINT
^t « *■ *
ROOM
HOUR
WINDOW
WALL
ROOF
FLOOR
DOOR
L I GHTS
. PEOP ( S )"^APPL ( S ) I\FIL(S)
^PEOPiL) APPL(L) INFILiL)
TOTAL(S)*
TOTAL ( L ) »
ROO.V-
TOTAL*
8
1^6.
105'*.
137.
0.
30.
0 .
0 .
0 .
0.
0 .
0 .
0.
.
0.
lo02 .
9
310.
.
119.
0.
61 .
.
244.
560 .
.
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0.
0 .
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10
535.
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113.
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o
(» NOTE — SENSIBLE TOTAL AND ROOM TOTAL FIGURES
AND SAFETY FACTOR. LATENT TOTAL INCLUDES SAFETY
INCLUDE PARTITION LOAD
FACTOR. )
, FAN HP.
HOURLY COOLING LOADS
ROOM 201 PRINT ROOM
(-^NOTE HOUR AVERAGING EFFECT)
Figure 6. Optional Cooling Load Hourly Printout
258
o
ROMIiNE f, SLAUGHTEKt If'iC. «* CONSULT liMG ENGINELKS
JOB 665/B
NRS/ASHRAE/APEC SYMPOSIUM »
FORT WORTH. TEXAS
SAMPLE PROBLEM 11/30/70 *♦ PAGE 33
ZONE — REPRO. 6 MAILING
nt -/r if --t a * «■ * a ;! -K « s -f. it -ft *n
PEAK LOAD DATA.
WINDOW
WALL
ROOF
PARTITION
FLOOR
DOOR
INF ILTRAT ION
LIGHTS TO RM
PEOP( 6.)
APPL I ANCES
FAN HP ( 0 . O'* )
SFTY FACIO.OO
ROOM TOTALS
TOTAL HEAT
SENS. RATIO
(^VENTILATION
^ TOTAL VENT
LT HEAT TO RA
ZONE TOTALS
GRAND TOTAL
SENS. RATIO
OCCURK ING
HEAT GAIN -
SENSI BLE
.
.
.
959.
.
226.
0.
.
.
.
.
0.
. (S)
AT
HOUR NO.
COOL I NG
LATENT
0.
.
.
. ( L )
16
HEAT LOSS - HEATING
LOSSES
293B .
.
.
.
.
666 .
.
INT. GAIN
CHECK FIGURES
I TOTAL HEAT I
0.
.
(H)
. +
. +
. +
. +
+ -
2 37 72 . ( I ) +
CCOLING( T )
38.4 BTU/SF
H.3 6TU/CF
312.2 SF/TON
HEAT 1 NG ( H )
33.1 BTU/SF
3.7 BTU/CF
30.2 SF/MBH
. (T=S+L)
0.891 ( S/T )
. (VS) . (VL)
7 2 1 4 1 . ( V )
783. (RA)
. (Z) . (ZD
. (GT=Z+ZL)
0.628 (Z/GT )
. (H)
. ( Vri )
. ( TH)
. I TH=H+VH I
783. (R
783. IR
COOLING(GT )
109.6 BTU/SF
12.2 BTU/CF
109.4 SF/TON
HEATING! TH)
133.2 BTU/SF
14.8 BTU/CF
7.5 SF/M8H
PYRAMID TOTALS
LIGHTS TO RM
LIGHTS TO RA
PEOPLE! 8.)
APPLIANCES
BEFORE DIVERSIFICATION
.*
783.*
.*
.*
.*
.*
. WINTER HUM I D I F I C A T I ON ( WH )
. TOTAL. WITH HUMID (THH=TH+WH)
. LOSS LESS INT. GAIN (TH-l-R)
822. WINDOW SOLAR GAIN
. NET LOSS — LESS INT. AND SOLAR
AIR UUANTITIES-
AREA
VOLUME
PEOPLE!* X D.F.
P£OPLE(SF/125. )
. *SF AT
. ♦CF AT
) 5. MAX. AT
8. MAX. AT
0.25 CFM/SF
2.00 CHANGES/HR
25.00 CFM/PERSON
25.00 CFM/PERSON
256. CFM.
3U7. CFM.
125. CFM.
204. CFM. !CFMPP LIMIT)
VENTILATION AIR SET EUUAL TO SUPPLY AIR ! ALL U.A.)
EXHAUST REQUIRED (NOT INCLUDED IN ABV
. CFM (FOR VENT LOADS)
«»«»»»♦»•»»
LOADS) = . »CFM
(WARNING - EXHAUST EXCEEDS VENT CFM)
INFILTRATION
o
0.»CFM (COOLING)
75.*CFM (HEATING)
SUPPLY AIR
ZONE PEAK LOAD
. *CFM,
■««»»«»*»«*
9.3 TONS
!NOTE -
AND TOTAL COIL AIR =
SUM OF ROOM VALUES)
. CFM (AT ZONE PEAK.)
*»««««*««« (D.T.R. = 25.0)
ZONE — REPRO. £, MAILING
Figure 7. Typical Zone Load Printout
259
ROM I ^iE
{, SLAUGHTER. INC.
♦» CONSULTING ENGINEERS
FORT WORTH
> TEXAS
* * * ft »
(^JOH 56b/B NBS/ASHRAE/APEC SYMPOSIUM *
SAMPLE PROBLEM 11/30/70 «* PAGE 34
HOURLY
COOL ING
LOADS, ZONE
— REPRO.
& MAILING
F I RST
SIX HOURS (SEE NEXT
PAGE FOR LAST SIX HOURS)-
HOUR
W I NDOW
WALL
ROOF
FLOOR
DOOR
PARTN
ZO.mE
LTS ( RM )
PEOP (S)
APPL ( S )
INF IL t S)
VENT ( S )
1 0 I I KM • S 1
10 1 I ^ N ♦ O J
GRAND
LTS( RA)
PEOP ( L )
APPL ( L )
INFIL(L)
VENT ( L )
TOT(RM.L)
TOT(ZN.L)
TOTAL
8
237.
.
149.
.
30.
959.
0.
0.
0.
0.
.
6 007.
107 3 7.
0.
0.
0.
0.
.
0.
.
.
9
blh.
.
130.
.
61 .
959.
560.
.
0.
.
•
3 .
hlO.
.
.
0.
.
.
.
.
10
9B^.
.
123.
1 344.
92 .
959.
S'+yi.
754.
.
0.
.
.
.
548.
.
.
0.
.
.
.
8 >
11
13a 5.
.
120.
.
123.
959.
o
.
948.
.
0.
.
.
.
626.
.
.
0.
.
.
.
.
12
129.
.
154.
959.
113&0.
.
.
0.
.
.
.
705.
13U6.
.
0.
.
.
.
.
13
.
.
291 .
.
185.
959.
.
.
.
0.
.
.
.
783.
.
.
0.
.
.
.
.
(NOTE-
-TOTALS
INCLUDE FAN
HP + SAFtTY FACTOR AS APPROPRIATE.
)
o
HOURLY COOLING LOADS —
ZONE
— REPRO. &
MAILINC
Figure 8. Optional Zone Cooling Load Hourly Printout
260
ROMIiME 6 SLAUGHTtR, IMC. ♦» CONSULTING ENGINEERS FORT WORTHi TEXAS
QjOB 565/B NBS/ASHRAE/APEC SYMPOSIUM « SAMPLE PROBLEM 11/30/70 »* PAGL 36
AIR SIDE ANALYSIS BY ROOMS. ZONE - REPRO. & MAILING
ROOM
IDENTIFICATION...
ROOM
SIZE. . .
ROOM CRM..
Ml NUTES
PER
FNL.
CALC
NAME OR...
AREA
VOLUME
VALUES. . . .
AIR CHANGE.
NO.
'JO.
OESCRIPTN.
SF
CF
CALC ADJ.
CALC.
ADJ.
#»« *
»*»»
■«■****#■&#*#
» * * « *
****
««#**
201
PRINT ROOM
192.
.
650.
3.0
202
MAIL ROOM
32U.
.
520.
6.2
203
MEN TOILET
192.
.
50.
30.7
204
WOMENS TLT
320.
.
240 .
10.7
TOTALS
.
.
.
6.3
REMARKS
■«■«**»»«*♦*«»♦
o
-( note: all rooms in this zone listed,
with appropriate data, whether
master or duplicate.)
O
AIR SIDE ANALYSIS FOR
ZONE - REPRO. & MAILING
Figure 9. Optional Additional Zone Printout
261
ROMINE & SLAUGHTER, INC. ♦« CO-\SULTlrMG ENGINEERS
(^JOe 565/8
N6S/ASHRAE/APEC SYMPOSIUM
FORT WORTH, TEXAS
SAMPLE PROBLEM 11/30/70 *♦ PAGE hi
BUILDIMG RECAP
»»»»»«*»•»*«♦»«■
BUILDING PEAK
WINDOW
WALL
ROOF
PARTITION
FLOOR
DOOR
INFILTRATION
LIGHTS TO RM
PEOP ( 90. )
APPLIANCES
FAN HP
SAFETY FAC.
ROOM TOTALS
TOTAL HEAT
SENS. RATIO
r^VENTI LATION
^ TOTAL VENT
LT HEAT TO RA
PUMP HP
BLDG TOTALS
GRAND TOTAL
SENS. RATIO
LOAD DATA,
HEAT GAIN -
SENSI BLE
it.
,
.
959,
H957.
926,
0.
,
,
.
.
.
, (S)
OCCURRING AT HOUR
— COOLING
LATENT
0.
NO. 17
HEAT LOSS
LOSSES
.
.
.
.
.
.
.
- HEATING
INT. GAIN
Check figures
(total heat)
.
.
.
. ID
.
,
(H)
. +
. +
. +
. +
+ -
. ( I ) +
COOLING(T)
27.1 dTU/SF
3,0 BTU/CF
442,0 SF/TON
HEATINGIH)
25.6 BTU/SF
2.8 BTU/CF
39.0 SF/MBH
. I T=S+L )
0.915 IS/T ]
. (VS)
. (V)
. (RA)
. (P)
. ( BS )
. ( VL )
. ( bL )
. (H)
3 . ( VH )
. ( TH )
U. (R ) +
. ( R ) +
COOLING(GT)
55.0 BTU/SF
6.0 BTU/CF
218.0 SF/TON
HEAT ING ( TH )
53.9 BTU/SF
5.9 BTU/CF
18.6 SF/MBH
. (GT=BS +BL )
0, 749 ( B/GT )
, ( TH=H+VH )
PYRAMID TOTALS
LIGHTS TO RM
LIGHTS TO RA
PEOPLE( 126,
APPLIANCES
GRAND TOTAL
AIR QUANTITIES
AREA
VOLUME
PEOPLE(« X O.F
PEOP, (SF/125.0
BEFORE DIVERSIFICATION
.*
.*
) .* .*
.* .*
,*
.
.
.
.
.
WINTER
TOTAL ,
HUMI DI FICAT ION ( WH )
WITH HUMID ( THH=TH+WH )
LOSS LESS INT.
WINDOW SOLAK
NET LOSS — LESS
GAIN (TH-I-R)
GA I N
INT. AND SOLAR
. «SF
. *CF
. ) 90. MAX.
) 89. MAX
AT
AT
AT
AT
0.25
2.00
25.00
25.00
CFM/SF
CHANGES/HR
CFM/PERSON
CFM/PERSON
.
.
.
.
CFM,
CFH.
CFM,
CFM,
TOTAL BUILDING VENTILATION, FOR ALL ZONES
446 0. ♦CFM
-********«**
-+ NOTE —
+ * = SUM OF
+ ZONE VALUES
(TOTAL BLDG EXH )
("= . ♦CFM)
o
INFILTRATION
75. ♦CFM, AT
499.*CFM. AT
1.00 FACTOR
1.00 FACTOR
75. CFM (COOLING)
499. CFM (HEATING)
TOTAL FAN AIR
, *CFM,
***«»**♦«*♦
BLDG. PEAK LOAD
51,5 TONS
AND TOTAL CUlL AIR = . CPM AT BUILDING PEAK
♦»«*****♦*♦
BUILDING RECAP
Figure 10. Typical Building Load Printout
262
Accuracy Requirements For Computer Analysis of Environmental Systems
R. . Cook and J. A. Serf ass
Power Systems Planning Department
Westlnghouse Electric Corporation
East Pittsburgh, Pa.
The difference between the actual energy requirement for an environmental
system and the energy requirement as calculated by a computer program is termed
error. The usefulness of such a computer program in selecting between alternative
systems is a function, in part, of the magnitude of the error. The total error is
considered in two parts - bias error that has the same percentage effect on all
systems considered, and random error that is unpredictable from one system to another.
The effect of error is quantified by assuming a uniform probability distribution of
random error between limits, and then calculating the probability that the lower total
cost system has been identified by the computer calculation. The evaluation of this
probability is accomplished by means of a simple decision tree analysis.
Key Words: Accuracy, competitive analysis, computer program, decision,
economic analysis, energy, environmental system, error.
1. Introduction
Most computer programs that calculate energy requirements of environmental systems in buildings
have been developed to aid in the choice between alternative competing systems. Important examples in-
clude the choice between energy sources, i.e., gas, oil, or electricity, and the choice between energy
conservation systems. Certainly there are other uses for energy calculation programs, such as the study
of physical properties of a system, and perhaps the use of energy calculations as an integral portion
of a computerized control system. The accuracy requirements developed in this paper, however, apply
only to the use of the programs to select between alternative systems or subsystems and do not apply
directly to other uses.
In the past, little consideration has been given to the relationship between the accuracy of
energy programs and the cost of using them. This paper presents such a consideration and should give
some insight into the answers of the following two questions: What is the expected accuracy? Does
this accuracy, combined with the result, justify the cost of the computer run? Precise answers to
these questions applicable to a specific situation are difficult to obtain. It would be necessary to
calculate the energy requirements for the various systems, construct a building with each of the systems
and measure the results over a period of years. Obviously, this is not practical. The purpose of this
paper, therefore, is not to permit the absolute determination of accuracy requirements, but rather to
permit some quantification of accuracy, based on estimated calculation errors, and the resulting value
of studies. Then, at least, users of building energy computer programs can begin to develop adequate
evaluations of their own use of such programs. In addition, and perhaps more important, it Is hoped
that developers of new programs can gain more of a feel for the accuracy required of their computer
programs.
2. Types of Errors
The errors that occur in the computer calculation of building energy requirements may be catego-
rized as either bias or random errors. Bias errors are those that have Idehtical percentage effects on
all alternatives and, therefore, on the differences between alternatives. For example, if the cal-
culations result in energy requirements that are 10 percent high for all alternatives, then the dif-
ference between any two alternatives will also be 10 percent high. Bias errors tend to occur in the
portions of the calculations that are the same for all alternatives, such as heat flow and weather
factors. Random errors are those that are unpredictable (within limits) between alternatives. For
Engineering Section Manager and Electrical Engineer, respectively.
263
example, the calculated energy requirements for one system may be five percent high, and for another
alternative, five percent low. Obviously for random errors, the percentage error in the difference
between alternatives can be vastly greater than the percentage random error in each alternative.
Neglecting bias errors, the actual value of energy consumption for a building system alternative
will be the calculated or expected value, plus or minus some random error. The probability distribu-
tion of the actual energy consumption about the expected value is some type of curve whose shape is
unknown at this time, but which probably peaks near or at the expected value. In other words, if the
random error is plus or minus five percent, then the probability of the actual value being five percent
above the calculated or expected value most likely is less than the probability of the actual value
being the expected value. The limited experience to date, however, indicates that within the expected
limits of random error, the curve of probability distribution is relatively flat. For the purposes of
this paper and to facilitate analysis, the probability distribution of random errors is assumed to be
flat between the random error limits, and equal to zero outside the random error limits.
3. Effects of Errors
The effects of random and bias errors can be visualized by means of Figure 1. "A" is the energy
cost for system A and "B" is the energy cost for system B. The lines about A and B represent the
actual values, which equal the calculated values plus or minus a random error of 10 percent, with no
consideration of the bias error. The calculated values of A and B are 1.0 and 0.6 respectively. Thus,
the calculated value of (A-B) is 0.4. Considering only random errors, the actual value of (A-B) can be
any value within (1+ 0.1) - (0.6+ 0.06) with the entire population of (A-B) being contained in the
parallelogram in Figure 1. It should be noted that the breakeven differential cost between A and B
(BEAC) is defined as the annual cost (excluding energy) of B minus the annual cost (excluding energy)
of A. If (A-B) (calculated) is greater than BEAC, then B is the apparent choice. The probability that
the actual value of (A-B) is greater than BEAC is equal to the shaded area of the parallelogram divided
by the total area. In Figure 1, BEAC is 0.3, and the probability that (A-B) (actual) is greater than
0.3 is 92 percent. Thus the probability that B is the correct choice is 92 percent. Similarly, if (A-B)
(calculated) is less than BEAC, then A is the apparent choice.
The effect of bias error is assumed to move the parallelogram to the right or left by an amount
equal to the product of the bias error and (A-B) (calculated) . This is equivalent to adding the same
product to BEAC. In Figure 1, if the bias error is expected to be plus 10 percent, then BEAC becomes
0.34 instead of 0.3. Thus the probability that B is the correct choice becomes 77 percent instead of
92 percent.
4. Probability Curves
The relationships described by Figure 1 were calculated for a^wj^de range of values of the dif-
ference in annual energy costs of alternatives A and B, shown as ("J^) > breakeven difference in energy
costs (BEAC), and random errors. The results are plotted in Figure 2 through 11. Note that each figure
contains a different family of curves which applies to one value of the relative closeness of the cal-
culated annual cost differential (A-B) and the breakeven cost differential (BEAC). The different
curves within a family apply to different values of the relative closeness of the annual energy costs of
each alternative. The abscissa is the random error of the energy calculations and the ordinate is the
probability that the more economical choice has been correctly identified by the calculation.
A-B
The proper curve is chosen by calculating ("~^) and BEAC, and finding the closest applicable param-
eters on a curve in the available families of curves. Then, knowing the approximate random error of
the energy calculations, one can find the probability that his choice is correct. This probability, of
course, is one measure of the relative usefulness of energy calculation computer programs in selecting
between systems. However, there is a need to relate the probability to economic factors, as will be
shown in the next section.
5. Maximum Acceptable Study Cost
Figure 12 is an elementary decision tree analysis illustrating the decision that must be made as
to whether or not to use an energy analysis computer program, and the chance events that occur after
the decision is made. For simplicity, it is assumed that there are only two alternative systems (A and
B) , but the same analysis could be expanded to include any number of alternatives, chance events and
decisions. In order to choose between two alternative systems, it is necessary to utilize either a
computer evaluation, at some expense, or an individual's own judgement which is assumed to be free. In
either case, a decision is made, presumably in favor of the less expensive system, and with the decision
is associated a certain probability that the correct choice was selected. When only judgement is used,
it is assumed that the individual making the decision is inexperienced in choosing between these two
systems, so there is a probability of 50 percent that he will select either system. This probability
could be adjusted to any expected value.
264
The total cost of each decision Is the cost of making the decision plus the equivalent cost of each
chance event, using the calculated expected value costs. The equivalent cost of a chance event is equal
to the summation of the products of the probabilities and the costs of all possible outcomes. The total
cost of an outcome must Include both the energy and the capital (including all other costs). Obviously,
all costs must be on either an annual basis, or a present worth or capitalized basis. Such a decision
tree analysis shows that the maximum allowable expense of a computer study is that expense which results
in the two decisions being of equal total cost.
Unfortunately, the decision tree analysis of Figure 12 cannot be used to evaluate a computer study
that Is yet to be done. The reason for this is that the computer study results are required for the
decision tree analysis. Its use, instead, is to evaluate the worth of past computer studies which, in
turn, should help in developing policies for future situations.
In order to account for variations in the accuracy of the calculations for energy costs, it is
necessary to add an additional term in the total decision cost. This is the "Evaluation of Risk of
Loss" in Figure 12. Its value is equal to zero, if the calculations are absolutely precise, and of
such a value that the acceptable computer cost is zero, if the computer results are very Imprecise.
Analysis will reveal that this is equivalent to replacing the expected total cost of the coinputer
selected system with a chance event. This chance event has a probability (P) of selecting the less
expensive system with its expected total costs, and (1-P) probability of selecting the higher cost
system with its expected total costs. (P) is the probability determined from the families of curves.
6. Hypothetical Example
The analysis approach developed in this paper can be illustrated by means of the following
example:
Alternative Calculated Annual Energy Cost Capital Cost
A $100,000 $400,000
B 80.000 535.000
A - B $ 20,000 - $135,000
In addition to the above parameters, assume a capital recovery factor of 0. (based on a 20 year
recovery period with a 10 percent interest rate), a bias error of (+) five percent, random error of
(+) five percent and a study cost of $5,000.
The breakeven differential cost between A and B (BEAC) is $15,900, on an annual basis. The ap-
parent choice is B, since BEAC is less than (A-B)(l-Bias Error) or $19,000. The use of Figure 9
(since + Bias error = 0.85) shows that there is a 75 percent probability that if we choose system
B, we ha^e^chosen the more economical system. The use of a decision tree analysis, adjusted for risk
of loss, with this probability of 75 percent, indicates that the breakeven cost for the computer study
would have been $9,000, on a first cost basis. This means that the expenditure of $5,000, in this
situation, for the computer study has resulted in a net savings of $4,000, and thus, the decision to
use the computer analysis was correct. It also indicates that the accuracy of the computer analysis
was adequate.
7. Appendix- Equations
Definitions: A - annual energy cost for alternative A
B - annual energy cost for alternative B
BEAC - annual costs (excluding energy) of B
less same for A
F - capital recovery factor to convert
capital costs to annual costs
RE - random error in energy -cost cal-
culations - per unit
BE - bias error in energy cost calcu-
lations - per unit
P - probability that calculations will
identify more economical alternative
SC - maximum allowable study cost (that
cost which will result in no basis
for using computer calculations com-
pared to the toss of a coin to choose
between alternatives A and B)
265
Equations :
If:
Then:
If:
Then:
BEAC ^ (A-B)(I-BE) - (A+B) RE
P = 1 that B is economic choice
(A-B)(1-BE) - (A+B) RE ^ BEAC ^ (A-B) (1-RE-BE)
^ , CbEAC - (A-B)(1-BE) + RE(A+B)]^
8 RE2 (A)(B)
that B is economic choice
(1)
(2)
(3)
If:
Then:
(A-B) (1-RE-BE) £ BEAC ^ (A-B)(I-BE)
, BEAC - (A-B)(1-BE) + RE(A)
2 RE(A)
that B is economic choice
(4)
(5)
If:
Then:
(A-B)(1-BE) - BEAC ^ (A-B) (1+RE-BE)
, (A-B)(1-BE) - BEAC + RE(A)
*^ ^ " 2 RE(A)
that A is economic choice
(6)
(7)
If:
Then:
(A-B) (1+RE+BE) ^ BEAC ^ (A-B) (1-BE)+(A+B) RE
, [(A-B) (1 -BE) - BEAC + RE (A+B
8~REMA)(B)
that A is economic choice
(8)
(9)
If:
Then:
BEAC - (A-B)(1-BE)+(A+B) RE
P = 1 that A is economic choice
(10)
SC
_(P-0.5)
F
(A-B)(1-BE) - BEAC
(11)
8. References
(1) Hertz, D. B. , Risk Analysis in Capital (2) Hammond, J. S. , III, Better Decisions with
Investment, Harvard Business Review, Jan-Feb. , Preference Theory, Harvard Business Review,
, p. 95. Nove-Dec, , p. 123.
266
NO SCALE
0 .2 .4 .6 .8 1.0
ANNUAL ENERGY COST - pu
Figure 1. Illustration of the effect of random and bias
errors on differential (A-B) energy cost.
267
268
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With eq (6) it is possible to set up a computation model as shown in fig. 1 , where
R, = R2 = ^ and R3
with F being the area of the segment.
The advantage of this model is that Rj and R2 truly represent the heat resistances. Resistance R3 is a
fictitious heat resistance representing the heat capacity of the segment divided by At. Other heat
resistances (see par 2.2 and 2.3) and the various heat sources (see par 3) may easily be joined
imaginarily with this model.
Eq (6) may also be written as a recurrent matrix equation:
290
A z(n) + B u(n) = C £(n-l) (7)
where z_(n) is a vector with temperatures Tj "^2,11' "^M.n*
u(n) is a vector with boundary conditions Tg^n ^M+l,n>
A, B and C are coefficient matrices of equation (6),
z(o) is the initial condition.
The solution of eq (7) is obtained by applying matrix inversion:
z(n) = A-'[C z(n-l) - B u(n)] (8)
By repeated substitution eq (8) passes to
n
£(n) = A-'C £(o) - 2 (A-'oI-'A"' u(1) (9)
1=1
Thus the solution zin) only depends on the initial condition z^(o) and the boundary conditions u(l).
2.2. Radiation Heat Transfer
The radiation heat transfer between two grey surfaces is described by the Stef an-Boltzmann law,
written in its technical form:
*rl2 = ('FeA,F]2(Ti^-T2^) (10)
where 'I'j-12 is the heat radiation flux from surface 1 to surface 2,
o is the Stef an-Boltzmann constant, Fg is an emissivity factor dependent on emissivities £] and 62 of
both surfaces and on the geometrical arrangement, Aj is the area of surface 1, F]2 is the configuration
or geometric factor defined as the radiation fraction leaving surface 1 which falls on surface 2, T] and
T2 are the absolute temperatures of surfaces 1 and 2.
If (T1-T2) = AT is small, eq (10) can be approximated by:
rl2 = 4aFeAiFi2T3AT (11)
- T,+T2
where T = — ^ — . Then the heat resistance for radiation Rj- for two surfaces 1 and 2 follows from:
AT 1
" (12)
*rl2 4aFeA,F,2TJ
When the temperature range is sufficiently smaU as by approximation in most cases of radiation transfer
in rooms, R^ will be a constant. Moreover for most room wall surfaces Fg^l, so that then R^- =
constant x -r— — .
AiF,2
The geometric factor F]2 for heat radiation between the wall surfaces of a room is calculated
applying well-known formulae. For perpendicular planes, indicated by 1 and 2, use is made of (fig 2):
F12 = (E,+E2+E3) (13)
with El = L arctg (1) + N arctg (i) - vP+lT arctg ( , ' ,„)
291
- 1 1 r (1+l2)(1+n2) l2(H-l2+n2) l2
^2 = ' 1" I ,^j^2+l2 (,+l2)(i2+n2)^
E = [ n2(1+l2+n2) j n2
^ (1+n2)(l2+n2)
and for parallel planes (see fig 3):
Fl2 = (E4+E5+E6) (14)
Er = y \/l+x2" arctg (-7=^=57) + x VT+y^ arctg (-~?tO
VI VI +y'^
Eg = -y arctg y - x arctg x
Radiation at the blades of Venetian blinds is a special case. For both heat radiation and the reflection,
absorption and transmission of solar radiation, several geometric factors were to be calculated. They
are indicated in fig 4 and formulated below:
FA(z,i/',m) = I - -r^ V'l+z2+2z+2z sin ^' + ^r-l— Vl + ( 1 -m)2z2+2z ( 1 -m) sin i/f" (15)
^ ' ' zmz zmz
where z = W/S, m is the part of W which is radiated by the sun, 4/ is the position of the blades. If the
blades are fully radiated by the sun then m = 1.
Furthermore:
Fc:(z.i/'.m) = TT— Vl + z2+2z sin \//' + -ir^ Vl+m2z2-2zm sin ii - v/l + ( 1 -m)2z2+2 ( 1 -m) z sin 1/'' - -r-^ (16)
^ ' ' 2mz 2mz 2mz 2mz
F5(z,i//,m) = { - [ V'l+m2z2-2mz sin i/- ' - 1] (17)
The factor F], F2 and F3 are special cases of F4, F5 and F5. When the whole blade is sun radiated then
F], F2 and F3 must be applied (m=l):
F](z,*) = Fi.izJ,]) (18)
F2(z,i/') = F5(z,./',1) (19)
Y^iz,^) = F6(z,i//,i) (20)
It is to be noted that
F4(z,i/',m) + F5(z,i/',1) + F(^(z,^|J,]) = 1 (21)
2.3. Convection Heat Transfer
At the various wall surfaces of a room convection heat transfer occurs. The heat flow between wall
and room air is, as usual, described by:
*^ = a^A(T^ - T3) (22)
where o.^, is the convection heat transfer coefficient, A is the area of the wall surface, T^ is the wall
surface temperature, T^ is the room air temperature. Thus the heat resistance for the heat transfer
between the wall surfaces and the room air may be presented by
^c=fe = ^ (23)
292
The convection heat transfer coefficient generally depends on the air velocity v and the
temperature difference AT. In case of room wall surfaces a useful approximation for is:
a = 2 + 6Vv for v < 5m/ s
(24)
= 6,5vO»S for v > 5m/s
V in m/s and in W/(m2.°C).
3. The Room Model
In paragraph 2 the simulation of conduction, radiation and convection heat transfer by a computation
scheme or network consisting of heat resistances and fictitious heat capacity resistances has been
explained. In figure 5 the computation scheme of the applied unit room is shown schematically. In this
figure the resistances drawn represent the convection resistances between the (numbered) nodes for the
surface and air temperatures, and some of the radiation resistances between the surface temperature
nodes. The other radiation resistances has been left out for clearness' sake. The blocks represent the
capacitive walls or layers. The figures in these blocks correspond to the segments in which the walls
are discretised. The complete room model consists of 71 nodes. Some detailed parts of this model are
given in figures 6, 7 and 8 referring to the schemes for the facade wall and for one of the various
possible glazing and sun shading constructions. The various resistance symbols are explained below fig 6.
For each node the heat balance equation can be written, containing the occurring heat fluxes, each
of which as a quotient of temperature difference and resistance, as described in par 2. The 71 nodes
equations together form the matrix equation (7).
4. Boundary Conditions
In this section the boundary conditions are described, such as the outdoor air temperature and the
solar heat sources in the room derived from the incident solar radiation.
4.1. Outdoor Air Temperature
The outdoor air temperature may be approximated by a single sinus function or by the sum of some
sinus functions. For suanner conditions in The Netherlands a useful approximation is:
Tao = 23.0 + 5.0 cos ^ (tg - 14) (25)
where T^q is the outdoor air temperature in °C and tg is the solar time in hours.
If sufficient meteorological data are available more accurate functions for T^^ can be obtained, for
instance the following form computed by Halahyja [ 10] , which is valid for Hurbanovo (Czechoslovakia),
July:
t„-14.6 t„-16.3 t„-9.0 t„-13.2
Tao = 22.06+7.38 cos 2n )+0.45 cos )+0,96 cos 2^ (-^ )+0. 1 1 cos(-^-^ ) (26)
4.2. Direct Solar Radiation
The direct solar radiation on earth, normal to the radiation direction, Sjj-j is generally considered
as a function of the altitude of the sun (h) and the sky turbidity (T). Using Nehring [ 13] the following
relation we derived:
Sdr(h,T) = Sdr max(T)(sin h)0.09T+0.14 (27)
with
Sdr max(T) = exp[ In 10(log S^r o-T/24.06)] (28)
where S^-j. q is the (direct) extra terrestrial solar radiation, normal to the radiation direction. The
altitude of the sun (h) is given by:
2v
sin h = sin 6 sin V + cos 6 cos 'P cos yT-(tg-I2) (29)
293
where 6 is the declination of the sun and 'f is the latitude on earth. If k is the k*-^ day of the year
then:
« = 27r sin (k-80)] (30)
For vertical surfaces S^j- must be multiplied by cos 4), where * is the angle of incidence.
4.3. Diffuse Radiation
The diffuse sky radiation is caused by the scattering of direct solar radiation in the atmosphere.
After numerous measurements for the diffuse sky radiation on a horizontal plane Bernhardt and Philipps
[ 1 4] derived:
Sdf,h = 0.33(Sdr o-Sdr)sin h (31)
The diffuse sky radiation on the vertical plane (Sjf y) depends, of course, on Sjf j,, but also on the
position of the sun in respect of the vertical plane in question. Threlkeld [ 15,16/ derived the latter
relation by investigation [ 16]. We approximated this relation by two polynoms:
Sdf h 0.560 + 0.436 cos * + 0.35 cos^* , for cos * > -0.3
' 0.473 - 0.043 cos * , for cos * < -0.3
is angle of incidence)
In fig 9 the computed diffuse sky radiation on the vertical plane is given as a function of the
altitude of the sun, with the azimuth of the sun with regard to the facade, as a parameter. Here the
turbidity factor T = 4.0.
Another part of the diffuse radiation on facades is caused by reflection of solar radiation by the
ground surface and by the adjacent buildings. The solar radiation reflected by the ground which falls on
a facade can be approximated by:
Sg = ^Rg(Sdr,h + Sdf,h) (33)
where R„ is the reflection factor of the ground surface for solar radiation.
4.4. Absorption and Transmission of Solar Radiation
at Glass Planes and Sunshading Surfaces
At the glazing and the sun shading devices the direct solar radiation and the diffuse radiation
fluxes are partly reflected, absorbed and transmitted. Thus the solar heat sources in the room are
activated (see fig 8). In order to calculate the various absorbed fractions, the properties of the glass
planes and sun shading elements must be known as a function of the so called profile angle [ 12] . For
this purpose the basic calculation method is taken from Parmelee [ 11,12].
Besides the properties of the separate glass planes etc , also the absorption, the transmission and
the reflection factors of the combined glazing and sun shading systems must be calculated. Here a
distinction must be made between direct solar radiation, diffuse sky radiation and diffuse radiation
from the ground and any surrounding buildings.
In the calculation of the (spread) solar heat sources in the various solar radiated surfaces, all
the above mentioned effects are taken into account.
Till now the calculation of seven combinations of ordinary glass with different sun shading devices
have been carried out. They are;
a) single glass
b) single glass with indoor blinds
c) single glass with outdoor blinds
d) double glass
294
e) double glass with indoor blinds
f) double glass with blinds in between
g) double glass with outdoor blinds
Glazings with sun absorbing planes are provisionally calculated in another way. For each plane the
absorption, reflection and transmission fractions for a mean incidental angle of 45° is applied. If
necessary these quantities are determined experimentally with the aid of a spectrometer.
Glazings with reflecting coatings, which are however as a rule slightly tinted, are calculated
while taking into account the dependence of the reflection and transmission on the angle of incidence.
The part of the incident solar radiation, which is transmitted through the glazing and sun shading
system which enters the room is spread over the various wall surfaces, in general homogeneously, if
necessary unhomogeneously.
4.5c Internal Heat Sources
In an office room in general heat is produced by occupants, the lighting (light flux, equipment heat)
dissipation) and any apparatus present. The heat fluxes produced are partly transferred to the air or
when the air temperature is controlled, they are added to the cooling load. Another part of the internal
heat load, however, is radiated to the walls and can partly be accumulated. Therefore the internal heat
fluxes must always be separated into a convection and a radiation part.
5. Survey of the Program
5.1. Possibilities
The units of the calculation model discussed in the former paragraphs are so built up to permit
murhvariants can be carried through. These variants refer to both the composition of the inner walls and
the facade and sun shading elements. Besides the diversity of glazing and sun shading systems, it may
for instance, also be assumed that the blinds may be drawn up during a certain period of the day.
Furthermore it is possible to calculate the point of time at which artificial illumination should be
switched on, on account of the computed visuable solar radiation flux that enters the room. Shading
effects caused by surrounding buildings or by overhangs and side fins may also be taken into account
[17].
Between the various capacitive layers of the walls cavities may occur, which may be ventilated. The
temperature of the ventilation air may either be prescribed or free. The room air may be ventilated with
outdoor air or with air of another (prescribed or free) temperature.
The temperature of the room air may follow a precribed curve, in which case the cooling load results
as a function of time. On the other hand the capacity of the cooler may be prescribed; then the room air
temperature is calculated as a function of time.
Besides the mean room air temperature respectively the cooling load, all the temperatures in all
the nodes are calculated. The heat fluxes between the nodes may be calculated if necessary. For indoor
climate analysis the radiant temperature at certain points in the room may be calculated. It is of course
possible to combine these quantities with the room air temperature, in order to calculate the so-called
dry resulting temperature.
5.2. Flow Diagram
In fig 10 a simplified flow diagram of the program is given.
The computing time of the program on a IBM 360/65 computer for one situation (room, facade,
sun shading, date, orientation, latitude) is about 5 minutes, subdivided in 2 minutes compilation time,
1 minute matrix inversion and 1 minute temperature and heat flux calculations when At = 15 minutes.
The core memory required is about 300 K oktades.
5.3. Test Results
In fig 11 and 12, some test results are given. In the case under consideration, the glazing con-
sisted of two normal glass planes, with Venetian blinds between these planes. As to the incident solar
radiation, the following data were chosen: latitude 52°, orientation SW, date July 23, sky turbidity
factor T=4. The internal load amounted to 800 W. The ventilation rate was three room changes per hour.
These results, and others, will be checked by means of an RC . network simulator.
295
6. Further Development
Several other variants as the above mentioned may. be included in the program through relatively
small modifications , such as a second facade with glazing, a separate ceiling part for lighting equipment,
a second non-transparant outer wall or roof.
For technical calculations, which must as a rule be carried out frequently, a reduced program will
be made, based on the same concept, with about 20 in stead of 71 nodes. Since the computing time is
nearly proportional to the third power of the number of nodes, then a reduction of the computing time
of about 30 times will be obtained.
7. References
[ 1] Buchberg, H. , Trans. ASHRAE No ().
[2] Parmelee, G.V. , Vance, P., Cerny, A.N. , Trans.
ASHRAE, No ().
[3] Korsgaard, V., Lund, H. , Publ. No 10 , Techn,
Univ. Danmark ().
[4] Euser, P., De Ingenieur (The Netherlands) 17,
63 ().
[5] Bordes, H.J., Heiz.-Lilft . -Haus techn. j_8, 300
().
[6] Boeke, A.W. , J. Inst.H.V.E. , 35, 195 ().
[7] Shirtlife, C.J., Stephenson, D.G., Techn. Paper
No 1 14 Div. Build. Res. N.R.C. ().
[8] Kusuda, T. Trans. ASHRAE 75_ (), Part 1,
No , p. 246.
[9] Boer, J.H.de, Euser, P., Int. Inst. of Refrig.,
Comn. II and VI, Liege ().
[10] Halahyja, M. , Ges.-Ing. 2, 42 ().
[II] Parmelee, G.V. , Aubele, W.W. , Huebscher, R.G.
Trans. ASHVE 54_. '65 ()
[12] Parmelee, G.V. , Aubele, W.W. , Trans. ASHVE
_58, 377 ().
[13] Nehring, G., Ges.-Ing. 83_, 185, 230, 253
().
[14] Bernhardt, F. , Philipps, H. , Abh.Meteorol.u.
Hydrol.Dienstes der DDR, 45 ().
[15] Threlkeld, J.L., Thermal Environmental
Engineering, (Prentice-Hall, ).
[ 16] Threlkeld, J.L. , J. ASHRAE - nov. , 43 ().
[17] Tseng-Yao Sun, Trans. ASHRAE, No , I. 1 . 1 .
().
296
297
Figure 3. The configuration quantities in case of parallel walls, used in eq(14)
298
outdoor^sgV
air
]— 1 -13
front wall
venti lation
]— 15-19
glazing and
sun shading
21 -
— ceiling
(n) = temperature of node n
A3-r52
part ition
walls
54-66
passage
wall
passage
air
floor
@
Figure 5.
The thermal model of the unit room (for clearness the radiation resistances
are omitted)
detai I see f ig. 7
indoor
air
Si
I — omnD — @)
S2
— fflnnn — (si)
S3
— mm — (67)
— iMD — (20)
Conduction resistances
Fictitious heat capacities
Convection resistances
— tiiiiiiiiiii — Radiation resistances
Convect ion +radiation resistances
(nj Temperature at place n
at time t+At
©Temperature at place n
at time t
Q^^Heat sources
Figure 6. The thermal model of the front wall
299
Figure 7. The computation scheme for a part of the front wall (for symbols see fig. 6)
300
Figure 9. The diffuse sky radiation on a vertical plane (S ) as a function of the
altitude of the sun for different horizontal positions of the sun (=) with
regard to the facade. Turbidity factor T=4.0
301
Start
jinitializatiorTI
read room
data
input data
print room
data
1
calculate
matrices
A, B, C
1
matrix
inversion A~'
read boundary
condit ions
control output
input data
print boundary
conditions
control output
are stated
figures
contradictory ?
calculate
initial
conditions x(o
lk=k+ 1
print
j,ves ^
wrong
data
1
stop
control output
Axj,+ 1 + Buj,+ , = Cxj,
3c+l = A~'(Cxj<. - Buj^+i)
calculate
boundary con-
ditions uj^+i
calculate
Xk+ 1 ' (Cxjt-Buj^+ 1 )
print and
plot resultt
output
yes / calculation with x^io
(another boundary condi-
\ tion?
yes
calculation with othei
room data?
stop
Figure 10. Simplified flow diagram of program arrangement
302
ty cr }■ -J ^ si' -f rtv rr, m <^g tvj (\ r>j (M r' fv (Vl
(- 0,- r- ^ t-i lt, o <; o '-r o sT (^i G .'^ f^' r- c r j r<-' r^i c >c c f»j >r ^ rvj or sj c •£ 'V' c in
f\| ^ fV (VI r ' f\j rsi fvj f\. ;v| r^: t\l r\j (V OvJ r^. p-i re (Vi r** 'O •^'^ rc^ m Ti r*"! (V ^N; r," rvj r^j o.; cm
/
area 75%
without cooling
-inside glass
temperature
■indoor air
4J
p
CO
4J
03
QJ
4J
■••• •
I- 'n rf LT < vc r- r- o- X c c
X 'J U" o O ^' C in O I."
—I -Vl ^ ~-' r -T
1^ c-
.~ m i.^ -j; ir
^ — 1 r^j r^. c
X or vc f C vC' iNj (V sC' a- O" ir, o vr x — i (^; o- ^ r- a- < O (v r<" ro a c lo vO sO cr cp co oc h o
I I I I I I I I I I I I I I I I I I I I I I
O O c- c- O C' C' — ' rj C en h- or
t CW- -f O CC h- ^ IX c C O o c- o c c o c> c. C/ o
* C' o C' o o c: c o c cr CT f-H vT vc CO vc in or c- c LT, cr> tv; cr o o o o o c c- o o o o o c o
--'r\J<:^a:(yccO"aOr-((\jr'"i>j^j-irir, ir-LTxir-t
/
/
area 75%
-cooling Load
-through ventilation
,1-
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4. Approximation of temperature variation by linear
eauation and the successive calculation metnod
of heat flow
By substituting eq.. (5) for (1), the heat flow response of the system H(t) to an
arbitrary temperature excitation Bit) is expessed as ;
ft ,
H(t) = e(T) • dt i- e(t=»v-^cf)
Jo
= Poem +Z[^%'(t:) &m €'''"'*''^^dT + ^H.o) Bn, e"^"*] + ^^Sc-c)^- 5"(-i-T)^T W
"»"<*■) — — —
The heat flow H(-t) is expressed as the sum of steady state term Y(t) , transient terms
XmCt) and impulsive term p(t) .
Now, let's assume the temperature variation 5c+) is approximated by a linear
equation within the time of tn 4 -t ^ tn+^t as seen in figure 5 and expressed as ;
= Ok-i^ + 02 rt) (5)
where ©,(+) = Q^t^
t « tn
0jf+) = 0
= 6h = const.
02ft) = A(»^^o (t- 1„)
/l(».»i> : temperature gradient ( deg • h~' )
Substituting eq. (5) for (^) the heat flow at the time ( tn a± ) will be ;
o
defined as follows ;
307
e-'c^ = 0 < It < t. i-/it
I fCTTV i'C-t-T^ ^^T = f(t) -t>o
Equation (6) becomes
In equation (7) the underlined portion is the same as the transient term Tim at the
time of tri . Thus the following simrle calculation method is obtained ;
= Bo ■ a-.) + /Icn.o B» 4t + ^ I Z«.(..:. "E™ +/!(«,.•, ■ Xm }-+ /l(n*l) (8)
where = ^'^"^^ = const. (9)
^"='1^^'"^''^'"^*^ = const. (10)
If we take the time interval of each section /i"fc to be the same as seen in figure 4
then the coefficient of and Xm. becomes constant and the calculation of eq. (8)
becomes very simple. It is also easy to change At by only changing E« and x».
whenever necessary.
This eq. (8) gives the rate of heat flow at the end of each interval so that we
are able to analyze the heating load or the temperature variations by substituting
this-for eq. (15) and it may be som^-what easier to understand but the following method
(which uses the quantity of heat flow during the interval instead of the rate of heat
flow at the end of the interval) would be more accurate in calculation.^'
3' Integration of heat flow in each interval
The quantity of heat flow durinf? an interval of tn ~ ( -v 4+ ) can be obtained
by integrating: eq. (7) with respect to Atr as follows (by using a variable of inte-
gration 1 instead of 4t ) ;
= 0w/3t + Z 4Z«<'«) ■ /I (11)
where 4Xo= [ -^^^ ^ { ^t- -i- ( , - e'/'-'S } + /-^t ] = const. (12)
^Z«(.,= Z.(«, (13)
If the time interval At is invariable after the time of tn as seen in figure 4 then
eq. (12) becomes constant and from eqs.(15) and (8) the follov/ing equation results ;
308
= /dZh.(«)-E„ + /A(»+o ilXm (1^)
where ^1 Xh, = ~ (\ - ^'^"'^'^ f (15)
= const.
If the temr^erature gradients A(n*<-> , yic-n^ « are known, each A2m(n*\) » ^Zmcntz)
can be easily calculated in succession by eq. (14), and each AHcx^n , 4Hc"«) »
is also obtained from eq. (11) by the repetition of sim];le calculations.
6. Equation of heat balance
( 'vhen the heat transfer coefficients of the room do not change )
Consider room k which is_ adjacent to ronms K = 1, 2, 5, where room air
teT.peratures are different from each other as seen in figuie 5« The follov;ing
equation of heat balance can be e'iven ;
<^k^^^^= V(t) - Hk(+) + Z [ Hh-rt) + 9 T^(t) { ©K(f) - 0fe«) n (IS)
where ©j, : thermal canacity of t ie air of room k (F4tr--fi- deg'' )
including that of furnis'iings of which the temperature change
is considered the same as that of the air temp.
, ©KCt) : temperature of the room and adjacent rooms
■^(•t) : heating rate supplied to room air (TJa-H-)
including axixiliary heat from human bodies and equipment
Hk(+) : heatloss through the surrounding walls of the room, where the
air temp, is 0fe(t) and the ad,''acent room air temp, is 6k(t) = 0
Hk(+) : inflow of the heat from the inside surface of the partitions
ad.jacent to the room K under the condition of 6k(.f)= 0
ad,iacent room Gxa)
Tk-C+) : air volume infiltrated from room^( outflow air is not related)
: specific heat of the air for unit volume CJVect -fi- deg '• m')
Assume the divisions of time aj'e the sa"ie as in figure 4- and assume the temperature
variations within the time interval ±n ^ (-tn ^'t ) are as follows ;
e(t.irt)= e
+ 6W(n-) ■ fecW -^t + Z. Zk-im(r.) + ^Xotri /Iwfn+O + JkiCd+o^t = 0 (22)
If the tenperature gradients Akfn+o , AK-jfff+o are not known, assuming that Ak , and Awtnto is /lw(«) , the temperautre gradient of tie wall surface ^ktcn+n is
obtained from eq. (22).
Step 2, Equation of heat balance of the room air
After the te^iperature gradients of the surrounding wall surfaces Ak^c«+o are
obtained the heat balance of the room air will be expressed as follows ;
= Zj Sf 0^HS('>*'1 4t I 6(fi(n) - fikCn) + ^ ( Aki(«tO " AkCi+n)}
+ I [Cp Tk(«+0 ilt I Sm-) - ek(h-, + y ( Alc(r.+n -yll,(«-o")\] +¥'k(i.tiv4t (25)
From eq. (23) the luiknown value of the temperature gradient Ak(M+o or the heating load
"Wkcn+o obtained.
8. Initial conditions of calculation
Figure 6 shows an example of the room air temperature variation of a flat house
which is built with reinforced concrete and is heated intermittently. As seen in the
example, if the thermal capacity of the system is large it will take many calculations
311
to eliminate the influence of inadequate initial conditions. Therefore , to minimize
the number of calculations, the setting of initial condition is important and the
following methods can be used.
8.1 To assume a steady state condition
One of a simple method is to make the initial condition of temperature of each
room as close to the mean daily temperature of each room as possible and assume a
steady state as in case 2 in figure 6, then the initial value of A'Zmw becomes 0.
8.2 To assu-ne 'ceriodical variation of temperature
vi/hen the temperature variation is aprroxiraated to a sine function as seen in
figure 7 then the value of z3 7".(ni becomes as follows ;
tn
P'" Bm +10 L / J
(24)
(25)
By using eq. (25) for the initial value of ^Zwcni at the time of fn , high accuracy
of analysis can be obtained with fewer calculations.
8.3 To chanp e the time interval of calculation
One of the distinctive features of this method is the easiness of changing At .
Thus by at first using a large At and rough calculations, much detailed analysis
can be done later as seen in figure 8.
To change the time interval Air to At' , we have to recalculate the new constants
AXo , Em sind Xm and replace the terms A'Zinx) with AZ^i'i as follows
Figure 9 shows a comparison of two cases A and B.
A : calculated by i^t = 0.25('6') from the bigining to the end
fa dotted line)
B : calculated by At = 1.0 till the 13th day and change to At = 0.25 C"^)
thereafter (a broken line)
The results agree peneccly after the 14th day. It will be also seen that if there
is a sudden change in neat supply and the time interval At: is large then the calcu-
lated te-iperature fluctuates for a while. However, from the nature of this inte-
gration method the calculatre.'i tempera^•u^e approaches an accurate value rapidly ana
even when it is fluctuating the average value or the integrated value of the results
over the several intervals is always accurate. And of course wrien t^.e variation of
excitation is contenuous or when an interval ^t is short theie is no trouble like
that.
For the system in which thermal capacitor is quite large, such as for the under-
ground structure, or when a synthetic effect of the syste-.s is in consideration, such
as a heating system and a room in which time constants are very different for each
other, the considerations of this sub-section are v-ry important.
Acknowledgement
This report is a summary and some extensions of the papers listed below.
The authors would like to acknowledge the continuing guidance and enco\iragement of
Dr. G. Hone.
312
References
1. N. Aratani,'N. Sasaki and M. Enai ; Continuous calculation method for the
analysis of room air temperature variations, Part 1 and Part 2,
Extra Report of A.I.J. (Oct., )
2. Same as above, Part 5, Extra Report of A.I.J. (Aug., )
3. N. Aratani, N. Sasaki and M. Enai^ A successive integration method for
the analysis of room air temperature or thermal load variations,
Bulletin of Faculty of Sng. , Hokkaido Univ., No. 51 (Dec, )
4. T. Maeda^ Some simplifications for the calculation of room air temper-
ature variations. Report of ^.I.J., No. 2? (195-4-)
5. T. Maeda, M. Matsixmoto and '-P. Naruse ; Simplification of the weighting
function refered to heating in concrete room. Trans, of A.I.J. No. 66
(Oct., I960)
6. P. Hasegawa ; Three methods in room temperature analysis. Trans, of a. I. J.,
No. 69 (Oct. , )
(Papers above are written in Japanese)
313
excitation
System
response
0n(t)=i'c
h(t)
e (t)
H(t)
Pig. 1
Thermal
system
©(t) = ei(t) + ejct)
Girt) = e
ft(^ ® — ^
1
° th tn-»/lt
Pig. 3 Approximation of temperature
314
K- 1
■fk
K-2
K-4
K= 3
Fig. 5 Room k and adjoining
room K
Ist day 2nd day Jrd day IJth day periodical steady state
O 24 48 72 312
Fig. 6 Intermittent heat supply and calculated room adr temperature;
315
t=0 tn
Pig. 7 Assuming of periodical steady state
Pig. 8 Change of time interval
13th day
Uth day
Hi
Hi
2n 304 312 320 328 C*^
Pig. 9 Examples of calculation when A t is changed
316
Digital Simulation of Building Thermal Behaviour
M. J. Wooldridge''
Division of Mechanical Engineering
Commonwealth Scientific and Industrial Research Organization
Highett, Victoria, Australia
The mathematical modelling of building thermal behaviour to predict transient
temperatures and humidities within it is presented in this paper The subdivision
of the building into thermally-independent regions, each comprising up to five
zones, each of uniform air temperature, is the initial step. Heat and moisture
transfer to or within these zones is then described mathematically. In particular,
the heat transfer through walls is traced by using finite element techniques. The
solution of the assembled equations has been programmed in Fortran IV. Boundary
conditions for each heat transfer path within a zone are compounded within the
calculation from the basic input data of external air temperature and solar radiation
(external boundaries) or internal radiative loads and solar radiation penetration
(internal boundaries). Occupancy, direct convective-to-air internal loads,
ventilation and infiltration variations may all be included as functions of time. The
program may be used to calculate either internal zone air temperature from a
knowledge of cooling or heating effect supplied, or zone cooling or heating load
required to maintain a specified internal air temperature profile. Test results
from two buildings are compared with post test simulations and reasonable agreement
between measured and calculated temperatures is demonstrated.
Keywords: Building, digital simulation, heat transfer, internal air
temperature, cooling or heating load, test results, thermal behaviour.
1 . Introduction
The creation of a mathematical model for whole or for part of a building in order to study its
thermal behaviour is a task now commonly practised in the air conditioning field [1 , 2, 3] 2. The
model may be relatively simple, amenable to hand calculation, or more complex, requiring digital
computing aids. That there is a use for such models is emphasized by the fact [4] that in the U. S. A. ,
for example, which itself accounts for 35% of the world's annual power consumed, a third of this is
expended on providing environmental comfort for people. Such considerations justify work aimed at
(a) generating more confident estimates of building cooling /heating / air- c onditioning
requirements ,
(b) allowing quantitative assessments of the more effective use of building properties,
(c) enabling more effective programming of installed plant.
The task of creating such a model was commenced during utilizing the digital computing
facilities of C S I R O. It was divided into two phases: initially a description of the heat transfer
aspects of building performance was attempted and secondly an extension to humidity prediction was
incorporated. The first phase is complete, the second is in progress and may be commented upon
during the Symposium.
Part of the material contained in this paper was presented [5] to the Annual Conference of
the Australian Institute of Refrigeration, Air Conditioning and Heating to whom acknowledgement is
made .
2. Modelling Technique and Assumptions
2. 1 Building Subdivision
Any part, or the whole, of a building may be divided into a number of discrete zones not
Senior Research Scientist.
Figures in brackets indicate the literature references at the end of this paper.
317
necessarily thermally isolated from one another, but possessing different distinguishing thermal
characteristics or boundary conditions. For example, inner and perimeter modules of a large
building, or rooms associated with north and south walls, would possess sufficiently different
boundary conditions to make them identifiable as zones. The choice of zones, in which the air
temperature is assumed uniform, is made by the user, and is, to a large extent, arbitrary. Such
zones form the coarse subdivision of the model: in each there are numerous heat transfer paths,
e.g. wall, window, betwe'en some source temperature and room temperature. These paths form
the basic elements of the heat transfer model.
The subdivision of a building into such zones is shown schematically on figure 1. This central
and peripheral configuration is the type of breakdown which might be employed for a storey of a
multi-storey building. On the other hand, a residential structure would require different subdivision
for analysis, such as is shown on figure Z. It is emphasized that, although it is often convenient to
do so, it is not mandatory to use zones identical to those of a particular air conditioning system.
It is the aim of the calculation techniques that, having established the model for any particular
building, the input of desired boundary conditions as a function of time may permit the output of
either air conditioning sensible load for a prescribed indoor temperature profile or the converse.
Later phases of the work will incorporate the moisture transfer processes and generate a more
complete air conditioning solution.
2.2 Model
The equation representing the balance of sensible heat transfer to the air within a zone may be
described thus : -
Cooling or Heating Effect from plant
+ Direct-to-air convective load (e.g. equipment, people)
+ Fresh air load
+ Surface-to-air convective load from all exposed surfaces within zones
= 0.
Using symbols defined in the list this equation may be written
JJ
QLS + QID + QSFA + I h. A. (T - T.) = 0 (1)
. , 1 1 ^ w. i' ^ '
J = 1 J
Figure 3 shows the situation schematically.
The calculation of building sensible load requires that QLS be made the subject of eq (1), thus
J J
- QLS = QID + QSFA + I h. A. (T - T.)
j - 1 ^
Considering each term on the right hand side individually, the first is derived directly from input
data on the number of people and their work rating and on the operation of equipment within a zone.
These are both permitted as functions of time in the input information.
The second, fresh air, term may be re-expressed
QSFA = HFA (T - T.) (2)
^ o 1 ^ '
where HFA is the product of a constant x fresh aii' ventilation and infiltration rates, and Tq and T^
outdoor and indoor air temperatures respectively. Again all parameters in this expression are
permitted as functions of time.
The third term is more complex to derive: finite difference numerical procedures are used to
solve the diffusion equation for each path from the individual boundary conditions for that path; hence
the inner wall temperature and convective flux is obtained.
The establishment of boundary conditions for each path at each integration interval is performed
318
within the program from input data of outside air temperature, solar radiation, shading and of internal
radiation and air temperature. It is in this fashion that radiation is introduced; that is, radiation,
be it long wave or short, is allowed to fall on the appropriate surface, be absorbed and ultimately
appear as a convective load to the indoor air. In this way both the thermal capacity of each heat
transfer path is accommodated and radiation is handled in the manner in which that mode of heat
transfer occurs in practice Thus the radiant contribution to load does not appear explicitly in the
results of the load calculation, nor is any factoring of radiant heat required.
In order to predict indoor air temperature, given a specified heating or cooling effect, Tj^ must
be made the subject of eq (1). Thus
QLS + QID + HFA . T + Ih. A. Tw ■
T. = ^ ° J J (3)
1 HFA + y h. A.
^ J J
Latent loads are also handled within the program. A simple calculation of latent heat gain due
to equipment, people and fresh air is calculated from the input data according to the practice of the
ASHRAE Guide [6]. If internal humidity is to be calculated simultaneously with indoor dry bulb
temperature, the increase in moisture level over the integration interval is assessed and combined
with the internal air dry bulb temperature to calculate relative humidity.
The whole calculation proceeds on a step-by- step basis in time, each time increment being
equal and determined from the building properties, which do not normally change with respect to
time. There are always an integral number of time steps to the hour and results are normally output
every hour. The maximum integration increment is 1 5 minutes.
The facility has been provided for the user to include the characteristics, including thermostat
operation, of an air-conditioning system when they cannot be expressed independently as input data
in the form of cooling effects.
2.3 Assumptions
Both diffuse and direct solar radiation (incident upon any surface) are calculated as a function
of time, either from total and diffuse radiation for a horizontal surface, which must be input in
tabular form, or from the expressions of reference [7]. A test is made at each time interval to
determine whether any path is in shadow: those in shadow are exposed to the diffuse and reflected
direct components, whereas those in the sun receive all components.
Long wave radiation is assumed to be incident on all external paths according to the product of
a coefficient hj^ and the difference between surface temperature, T.^ . and the mean radiant tempera-
ture, Tj^. (Tj^ - Tq) may be input as a function of time. ^
Any radiation passing through the windows of a zone is assumed to be incident on and wholly
absorbed by the floor of the zone. Internally generated radiation is apportioned to each path of a
zone according to an input form factor.
Thus we may create a forcing or source temperature on the path boundary remote from the room
and a sink temperature on the room side boundary
Q + h (T - T )
T = T + — ^ (4)
source o ^v, + h
"rsink - ^1^ IT
1
These temperatures are analogous to the sol-air temperature [6] and are derived from a defining
equation of the type
K ' ^r) (^3,,,,, - T^) = (T^ - T^) + Q3 + h^ (T^ - T^)
where T.^ is the wall temperature of any path.
319
Internal paths either wholly within a zone or separating two adjacent zones are permissible.
Both source and sink temperatures are defined by equations of type (4) above for such paths.
All paths are assumed homogeneous in the direction of heat transfer so that they possess the
properties of a uniform medium in that direction. Later stages of the study will enable non-
uniformities to be modelled more exactly.
The building thermal model, including its boundary heat transfer coefficients, is not permitted
to vary as a function of time. Again, later stages may permit some variation of these coefficients.
3. Applications
3. 1 Test Building
Experimental data from two different test periods has been taken to illustrate comparisons of
temperatures measured and predicted within a fairly heavy two storey office building. Curves are
included on figure 4 illustrating these comparisons. Further work on this aspect is continuing, but
agreement in these tests is considered encouraging.
3.2 Examples of Use
Two hypothetical buildings in Sydney have been chosen to illustrate the calculation of air
conditioning sensible load, under normally imposed design climatic conditions and under measured
severe climatic environments. The normally-used design dry bulb of 32°C has been adopted to
perform a load calculation by the ASHRAE Guide method for both an 1 8 square brick veneer residence
and for a typical storey of a city office building. Maximum sensible space loads (excluding fresh air)
of 8. 5 kW and 83 kW respectively, for a constant indoor dry bulb temperature of 24'-'C, were deduced
from this approach. The computer model for each building was fed with climatic data from the three
hourly Commonwealth Bureau of Meteorology readings on magnetic tape for Sydney. Heatwave
periods were input for the hottest spell in the ten years (-) on record and for the spell
containing a maximum dry bulb exceeded only 10 times during that period. Clear day solar radiation
was input for these spells being calculated by a method [7], previously described by the author.
Figures 5 and 6 show how the sensible space load of the office storey varied with time during these
spells. The difference between the once - in- 1 0 -year maximum and the once-in-a-year maximum is
significant, the latter amounting to 93% of the former. A comparison is summarised in table 1 below
for both the residence and the office buildings.
There are substantial differences between the cooling calculated from the transient thermal
model and from the ASHRAE Guide quasi- steady- state approach. However, it is not advocated that
actual climatic sequences be used for design purposes: that would require far too much analysis. It
is proposed to develop design sequences using a transient mathematical model to test for frequency
of load occurrence, but this will be the subject of a separate paper. At this time, these examples
are included to illustrate uses of the computational model.
Table 1. Maximum sensible coolings loads for
3 different external environments (kW)
Sydney Building
ASHRAE Guide
PRESENT
Once in 10 years
METHOD
Once in a year
Max.d.b.t. 32°C
Max. d. b. t. 42. 2°C
Max.d.b.t. 38.2°C
18 sq . Residence (167 m^)
Space load
People, Equipment and fresh air
TOTAL
8. 5
2. 0
10. 5
6. 4
2. 3
8. 7
5. 0
2.2
7. 2
Storey of Multi- storey block
Space load including people,
equipment
Fresh Air
TOTAL
83. 2
14. 4
97. 6
70. 6
31 . 4
102 . 0
65. 7
24. 3
90. 0
320
An alternative calculation on the above office building illustrates the Use of the program in
predicting air temperature. Indoor air temperature has been estimated over a three day design
period for three levels of constant cooling effect, at 50, 75 and 100% of maximum required by the
calculation for constant room temperature of Z4°C . Figure 7 illustrates the temperature profiles
obtained: from these it may be observed that, standby and pull down considerations aside, a some-
what smaller plant could still generate comfortable conditions. It is, of course, easy to examine the
indoor temperature profile under any occupancy loading and after periods of shut down over weekends
say, so that better informed planning of standby and pull down requirements is possible.
4. Conclusions
It has been the aim of this paper to present a broad outline of the mathematical modelling pro-
cedure for the prediction of building thermal performance now set up at the CSIRO Division of
Mechanical Engineering, and to illustrate some of the validation and uses.
While the experimental validation is continuing on larger buildings, the results obtained so far
are sufficiently promising to suggest that the model is reliable.
Results of applications attempted so far indicate that, by being able to simulate correctly the
heat diffusion process and by inputting radiation so that it is first of all absorbed, the part of a
building thermal load transmitted via the structure to the air may amount to only some 75% of that
predicted by conventional quasi- steady state methods.
The power of the modelling technique in being able to estimate indoor temperature excursions
for many varieties of input enables an investigation of the effects of different building properties or
of modes of operation of cooling or heating plant.
5. Refe
1 Stephenson, D. G. , Method of determining
non steady state heat flow through walls and
roofs of buildings, JIHVE, May .
2 Stephenson, D. G. and Mitalas, G. P. ,
Cooling load calculation by Thermal Res-
ponse Factor Method, Trans. ASHRAE, 73
().
3 Boeke, A. , New developments in the
computer-design of air conditioning systems,
JIHVE, October .
4 Jordan, R. , Environment Control of
Enclosed Spaces , Fed. Conf. Aust. Inst, of
R. A. H. Melbourne, April , Paper No. 4.
ences
5 Wooldridge, M. J. , The prediction of building
thermal performance. Federal Conference
Australian Institute of Refrigeration, Air
Conditioning and Heating, Melbourne, April
1 970, Paper No. 6.
6 ASHRAE Handbook of Fundamentals,
Chapter 28 ().
7 Wooldridge, M. J. , Solar radiation and its
effect on air conditioning load. Paper delivere
to AIRAH S. A. Division, November 28th .
To be published as Division of Mechanical
Engineering Report E. D. 13.
6. Notation
Symbols
A - area
h - heat transfer coefficient
HFA - = constant x fresh air flow rate from
both ventilation and infiltration
JJ - Total number of heat transfer paths
per zone of building
Qg - Short wave radiation x path absorptivity
Ql - Long wave radiation x path absorptivity
Qj- - internally generated radiation
intensity x path form factor
QLS - sensible load for cooling and heating
QID - internally generated direct convective
load
QSFA - fresh air load
T - Temperature
t; - glass transmissivity
Subscripts
j - path identifier
i - indoor condition
o - outdoor condition
R - long wave radiation
W - wall
Source - external boundary layer forcing value
Sink - internal boundary layer forcing value
d - directional
n - non-directional
321
FLOOR AND
CEILING
WINDOW
EXTERNAL WALL
INTERNAL WALLS
(INTER-ZONE )
INTERNAL WALL (INTRA -ZONE)
1. Schematic of Building Plan Subdivision into zones.
2 BEDROOMS
AND
BATHROOM
KITCHEN
LDRY. ETC.
LOUNGE
ROOF SPACE IS ZONE 5
2. Typical Zonal Subdivision for Residential Building Analysis.
322
\
DIRECTIONAL
RADIATION.
CONVECTION
CONVECTION h,.T,
^ I CEILING ( PATH TYPE 2 )
EXTERNAL WALL /
( PATH TYPE 0 ) ^
INTERNAL
RADIATION
a..
2
/ / J / /t/ / / ^ / / ^ ^
/
CONVECTION
DIRECT TO AIR
a.
RADIATION V
NON DIRECTIONAL*
LONG WAVE
ADJACENT
ZONE L
■ PARTITION
(PATH TYPE 3 )
CONVECTION
T. (:T. )
COOLING
^ EFFECT
^ a..
FLOOR
(PATH' TYPE 1 )
h,. T,
3. Schematic of Incident Heat Fluxes for Typical Building Zone.
16-
0 10 20 30 40 50 60 70 80
TIME - HOURS
4. Measured and Predicted Air Temperature Profiles for an office building in Melbourne.
323
DESIGN FIGURE BY ASHRAE GUIDE
-300
■^3 ' ' ' ' ' '
23JAN 24JAN. 25JAN 26JAN. 27JAN 28JAN 29JAN. 30JAN. 31JAN
DAILY MAXIMUM
DRY BULB TEMP.
I 1 23-3 'C
>. J 74 0 'f
310
880
393
40-9
105 9
42-2
108 3
39'S
103 4
2S'S
78 0
23-8
750
255
780
5. Sydney Office Block - Typical Storey : Estimated Sensible space cooling load
for period 23 - 31 Jan. I960. (Maximum dry bulb temperature on 27 Jan. I960
never exceeded during - 65)
DESIGN FIGURE BY ASHRAE GUIDE
24 NOV. 25 NOV 2(NOV 27 NOV 28 NOV. 29 NOV 30 NOV 1 DEC. 2 DEC 3 DEC.
DALY MAXIMUM 1 22-1 "c 27-7
DRY BULB TEMP.
1 22-1 "C 27-7 38-2 22-7 24-4 22-7 22 7 37-1 20 5 24 (
J 72 0 V 12 0 WI'O 73 0 70-0 73 0 73 0 W 89 0 77 0
6. Sydney Office Block - Typical Storey : Estimated Sensible space cooling load
for period 24 Nov, - 3 Dec. . (Maximum dry bulb temperature on
26 Nov. exceeded 10 times during - 65)
324
THIRD DAY OF DESIGN SEQUENCE
7. Sydney Office Block - Typical Storey : Estimated Mean Air Temperature for
3 different (constant) applied cooling effects.
325
A Computer Programme for the
Calculation of Individual Room Air
Temperature of Multi -Roomed
Buildings
1
K. R. Rao and Prakash Chandra
Central Building Research Institute
Roorkee, U. P. ,
INDIA
In recent years the use of computers for the calculation of heating and
cooling loads and for the prediction of indoor air temperatures of buildings
has been well established and is in the increase. Many organisations in a
number of countries have developed suitable computer programmes in accor-
dance with their specific requirements and the computer facilities available.
Most of the programmes which are meant for the calcvdation of indoor air
temperatures of the unconditioned buildings, treat the whole building as a
single enclosure. However it is also of practical interest to determine the
individual room air temperatures within a multi -roomed building. For this
purpose a computer programme which is siiitable for a small machine like
IBM digital computer with 60K memory has been developed. This
programme takes into account the orientation of the rooms, ventilation,
internal heat sources, internal mass and furnishings and solves a set of
linear simultaneous equations for obtaining the indoor air temperatures of
the individual rooms. Provision has also been made in the programme to
determine the inside surface temperatures of walls, roofs and floors, mean
radiant temperatures and the heating and cooling loads of individual rooms,
if desired.
The main programme utilizes a good deal of precalculated data obtained
by a number of separate programmes developed for the calciilation of sol -air
temperatures, shade piatterns of overhangs and fins, solar heat transmission
through glass and frequency response characteristics of building sections.
Key Words: Computer programme, driving point admittance function,
Fourier analysis and synthesis, heating and cooling loads, heat trans-
mission coefficient, matrix equation, non-structural heat gains, room
air temperature, shade patterns, sol-air temperature, surface tempe-
rature, transfer admittance function.
1. Introduction
The problem of determining the thermal response of bxaildings under any given climatic
conditions has drawn the attention of many research and industrial organisations the world over
With the ever increasing use of digital computers, in all most all branches of building science,
the computational methods, which were earlier considered as unmanageable, are now finding wi
Scientist and Senior Scientific Assistant, respectively.
327
application. This trend is more evident for the problem of the calculation of inside air temperatures
and heating and cooling loads of buildings exposed to variable weather conditions.
In the last decade several computational techniques, which are specifically suitable for high
speedy machine calculations, have been evolved by various researchers in the field of Heat trans -
fer(lf'(2) (3) (4). A number of computer programmes for the accurate estimation of heating and
cooling loads and the indoor air temperatures have also been reported (5) (6) (7) (8). However,
almost all of these programmes treat the building as a whole as a single enclosure and do not account
for the variations of temperatures of the individual rooms within the building. The present paper
deals with a method and a computer programme developed for the calculation of individual room air
temperatures of multi. -roomed buildings.
2. Factors Involved in Room Air
Temperature Calculations
In order to determine the thermal behaviour under a given climate, a large number of factors
are to be taken into account. These factors can conveniently be grouped into three categories,
2. 1 Climatic Factors
(a) Diurnal variations of shade air temperature
( b) Solar radiation (direct and diffuse)
( c) Net low temperature radiation exchange
( d) Wind speed and direction
( e) Humidity
2. 2 Design Factors
(a) Thermal characteristics of building sections i.e. walls, roof, ceiling, floor, doors,
partitions etc.
( b) Surface radiation characteristics i. e. absorptivity, emmissivity and transmitivity of buil-
ding sections
( c) Shape and Orientation of the building and internal layout
(d) . Window design, number, location and type of glass areas
(e) External and Internal shading devices such as overhangs, fins, louvres and venitian blinds,
curtains respectively
2. 3 Utilization Factors
(a) Ventilation
(b) Internal heat sources and sinks
(c) Density of occupancy
(d) Living habits which influence (a), (b) and (c).
The complexity of the problem increases not only due to the large number of variables that come
into the picture but also due to the interactions between them.
3. Computational Method
As buildings are subjected to periodic variations of air temperatures, solar radiation and other
climatic elements, the inside air temperatures of buildings would also fluctuate periodically. Seve-
ral methods have been developed for determining the thermal response of building elements (9) (10)
(11). Of these the transfer Martix method of Van Gorcum (12) for the determination of periodic heat
flow through a homogeneous slab has gained popularity being well suited for high speed digital compu-
Figures in brackets indicate the literature references at the end of this paper
328
tations. The Matrix method was further extended by Muncey (13) for predicting indoor air tempe-
rature variations of a sj.ngle room. In this approach, the bounding elements of the enclosure are
taJcen as parallel heal/paths and the internal temperatures are computed by applying the principle
of heat balance for steady as well as harmonic parts.
The equations for indoor air temperature variations (14) can readily be expressed in terms of
areas, sol -air temperatures of exposed surfaces, steady state heat transmission coefficients
(U values), transfer and driving point admittance functions of building sections, ventilation rate
and internal heat sources and are given below.
t +
la
la, h
Cos (wj^r -city for the former is about one-fifteenth as small as the latter.
It It^p also been found that this method is useful to obtain the effect produced
by an addition of rooms.
It is obvious that this method is also useful for obtaining the heating load and
cooling load.
340
341
7
6
5
4
3
2
I
0
(
7
6
5
4
3
2
I
0
I
X
1 Kcal-Hr
20 40 60 80 100 120
Time (Hour)
140
160
180
200
Room air temperature of 2-rooms resulted from heating in the furm of a
step function at X-room.
342
Figure 3 Room air temperature of 5-rooms in parallel resulted from heating in the
form of a unit step function at X-room.
343
344
simulation by Digital
Computer Program of
the Temperature Varia-
tion in a Room
G. Brown
The Royal Institute of
Technology
Stockholm, Sweden
A computer program has been developed at the Royal Institute of Technology,
Stockholm, Sweden, capable of calculating the temperature variations that occur in a
room subject to variable internal and external heat gains. The program offers a very
flexible choice of the quantities that are to be calculated. The air temperature in
the room, the temperature and supply volume of the ventilating air, and the capacity
of the heating or cooling units in the room can either be calculated separately, or
in pairs when the limiting values of both quantities are known.
The program solves a system of heat balance equations which take into effect
surface heat transfer by radiation between the room surfaces, by convection between
the room air and room surfaces, and by conduction between the different material
layers of the walls and floors. Not only is the temperature of the room air calcu-
lated, but also always that of the room surfaces and the material layers and outside
surfaces of those walls and floor slabs which enclose the room. This practice has
proved to be valuable when using the program in connection with studies of different
types. When an operative temperature is to be determined, the temperatures of the
different surfaces in the room must be given, in addition to the room air tempera-
ture. The calculated temperatures on the outside surfaces of the walls and floor
slabs which enclose a room come into play in connection with studies of the function
of temperature control systems in adjacent rooms having different temperatures due
to different heat gains. An example of this is given in the article.
Key Words: Absorption factors, ALGOL, choice of unknown variables, daylight
distribution in rooms, digital computer program, finite-difference method,
heat balance equations, operative temperature, temperature control, tempera-
ture variation in a room.
1. Introduction
Use of computers in the study of non-uniform temperature variation in buildings began rather early
in Sweden. The first example of such use dates from when a method was described for computer cal-
culation of the temperatures in an external wall exposed to solar radiation /I/. In the same year an-
other investigation was presented dealing with design outdoor temperatures for heating load calculations
HI . The temperatures proposed in the survey were determined on the basis of computer calculated tem-
perature variations in different types of buildings with temperature variation out of doors. In both
these cases, the calculations were made on the Swedish computer BESK which was installed in .
The equations on which the present program is based were first published in /3/. Since this
date, the program has been developed in order to make it more versatile, cheaper, and easier to use. It
has thus been supplemented in such a way that the quantity which is to be calculated can be chosen from
among several different variables. By revising the program, which is chiefly written in ALGOL (except
for a lesser part in internal computer code), and by modernizing the computer itself, i.e. the Swedish-
made TRASK, the cost of computer time has been decreased. For a normal case, it costs, at present, about
US $ 10 for the calculation of a 24 h period of variation in one room.
A special alternative for easy use of the program has been developed in the form of the "engineer's
version" and enables the calculations to be made with less work, especially concerning the presentation
of data since the data need not be presented on special forms. The complete program version described
in this article allows, however, greater flexibility concerning the choice of variables.
345
The calculation method, which is an iterative, finite-difference method, has been developed with
respect to its application for the dimensioning of plant for cooling and heating rooms, but also for the
study of how buildings should be constructed in order to provide a comfortable thermal environment at
the lowest cost. It should be possible to use the program both for design and for research and investi-
gation work. In view of the fact that it is essential to be able to explore the effect of all factors
which may arise, the complete program version is so written that no material constants or values for
temperature and incoming radiation are stored in the computer memory. Furthermore, there are no limita-
tions regarding the definition of the surroundings of the room, i.e. its position in the building.
To date, the program has been used in a fairly large number of cases in connection with the design
of hospitals, hotels and office buildings. Further, the program has been used in a survey concerning a
design guide for school buildings in the study of the effects of different factors on classroom tempera-
ture. The investigation resulted, among other things, in a proposal for a standard for calculation of
the temperature in classrooms for design of school buildings throughout Sweden. According to the propos-
al, such calculations will involve the use of the program presented here, or a program giving the same
result /4/.
2. Input Data
Data for the calculations is recorded on eight different types of forms: 1 Room, 2 Wall or floor,
3 "Facade", 4 Window, 5 Lighting unit, 6 Heating unit, 7 Time dependent data, and 8 Constants. Time
dependent and time independent quantities are differentiated, see table 1. The time dependent quantities
can be assigned variable values during the calculation period, i.e. the time period under which the cal-
culation is considered. They are identified on forms 7 and 8 by numbers assigned to them from forms 1-6.
A form of type 7 can be used to record the values of a given quantity at different time points, while a
form of type 8 is used to record data for such quantities which are in principle time dependent but which
for the present case do not vary with time.
The room is assumed to have parallelepiped shape. Forms of type 1 contain a sketch of a room in-
cluding a coordinate system enabling the addition of sub-surfaces. Such sub-surfaces are windows and
lighting units and even heating units which emit thermal radiation and therefore need to be included as
surfaces in the room.
Values of outside air temperature and radiation from the sun and sky are found from tables or dia-
grams. The tables used here are computer calculated and based on Finnish measurements /5,6/. They give
sun and sky radiation against vertical facades and horizontal roofs as well as radiation transmitted
through vertical and horizontal windows with double-glazing of ordinary window glass. The radiation re-
flected at the ground is included in the radiation values. In cases where a facade falls within the
shadow of surrounding buildings a separate program is used to calculate the portion of the day when the
different windows in the facade are sunlit. Computer drawn diagrams are used in determining the incom-
ing radiation through windows which are shaded by overhangs or which are set back from the external plane
of the facade.
The shading coefficients (tab.l) give the transmission through the fenestration in question in rela-
tion to the total radiation energy transmitted through a double-glazed window of ordinary window glass
ni. These coefficients are determined under the assumption that the surface heat transfer coefficient
for the exterior side of a double-glazed window is 16 and 8 Wm~2deg-1 for the interior side.
The thermal resistance of the interior side of a window is not included in the calculations since
the temperature of the window surface towards the room is included in the programmed heat balance equa-
tions .
Shading coefficients and thermal resistance of windows are listed in table 1 as time dependent quanti-
ties since these values are not constant for windows having drapes or Venetian blinds which are used for
only part of a 24 h period.
The word "facade" is taken to mean the exterior side of each wall or floor for which incoming radia-
tion, surface heat transfer coefficient, and air temperature are known. Thus a "facade" is not necessar-
ily the outside of an exterior wall. It can just as well be the outer surface of a roof or of a wall
giving onto a corridor.
A form of type 6 is used to designate a heating or cooling unit whose surface radiation or thermal
capacity must be taken into consideration. Furniture can be considered as such heating units of effect
0. For convective heating units with no thermal capacity, the data is instead listed under "heat direct
to room air". Heat from persons present in the room is often listed under this variable.
Radiation from people can be introduced in the calculations in the form of radiation from a lighting
unit which is located on the floor. The amount of body heat given off decreases with an increase of temp-
erature. The program can simulate lower convective heat radiation when the calculations indicate a higher
air temperature.
346
Table 1. List of quantities in the computer program.
Type of
data or
number i
form on which
identification
s given
Time independent quantities
Time dependent quantities
Type 1
Room
Length, width and height of room. Sub-
surface dimensions in x-and y-direc-
tions and coordinates for their lower
left hand comers. Reflectance for
room surfaces and sub-surfaces.
Outside air temperature, volume of
air leakage, room air temperature,
ventilating air temperature, volume
of ventilating air, heat direct to
room air. Unknowns.
Type 2
Wall or
floor
Thickness, coefficient of thermal con-
ductivity, density and specific heat
of different layers of materials of
the wall. Thermal resistance of air
layer in the wall. Number of partial
layers of each material layer.
Absorptance of facade surface.
Cloudiness .
Type 3
"Facade"
Radiation towards "facade . Air
temperature. Surface heat transfer
coefficient .
Type 4
Window
Radiation transmitted through double-
glazed windows. Shading coefficient
for total and for direct transmitted
radiation. Thermal resistance. Out-
Type 5
Percentage of radiation from lighting
Lighting effect.
Lighting unit
units .
Type 6
Heating unit
Volume of heating or cooling unit,
density and specific heat of the
material of the unit. Surface en-
larging factor of the unit.
Effect of heating or cooling unit.
3. Unknowns
Those variables which may be unknown are room air temperature, ventilating air temperature, volume
of ventilating air, heat direct to room air, and effect of heating unit. The variable which is to be
calculated is determined in the program by the code number given to "unknowns". Code numbers are listed
on the forms in the same way as the values for other time dependent variables. The code number gives
the different positions in the program where the sought variable is solved from the heat balance equation
for the room air.
It is sometimes desirable to seek a variable given the conditions that it lies within certain limit-
ing values. If the calculated value is larger than a maximum value or less than a minimum value, then
the value for another variable must be found. Thus the program first tests a variable against its limit
value (which is not necessarily constant during a 24 h period). If this limit is crossed, the position
of another variable is found, the result is calculated, and the first variable is given its limit value.
4. Thermodynamic basis
4.1 Angle and Absorption factors
The equations for heat transfer between room surfaces take into consideration reflexion of short
wave radiation (from the sun and sky) but not long wave radiation. Thus it is assumed that all long
wave radiation which is emitted from a surface A^ and which meets a surface Aj is totally absorbed by
A j . Emission is furthermore assumed to occur diffusely and transmitted energy is determined by the
angle factor , which is calculated using generally known equations and methods, see e.g. /8/ and /9/.
Transmitted radiation energy for short wave radiation is found by the equation system
m
i;;..=cp..a. + Z cp. r ii .
ij iJ J i-P P PJ
Here V^. is the absorption factor for radiation between A. and A., a. is the absorptivity of A.,
r is the reflectivity of some surface A of the m room surfaces, and^l- .^is the absorption factor ^for
radiation between A and A . The first tirm of the expression for t . . ii^that portion of radiation from A.
which IS absorbed at A. and which has not been reflected by any inte^ediary surface. The sum term is ^
that radiation absorbed by A. which has first been reflected by the room surfaces.
347
In cooling load calculations it is useful to know at which time daylight is so weak that light-
ing units must be turned on. The equation system above has been used in the study of daylight distribu-
tion in rooms in this context, the program having first been extended so that the absorption factors for
radiation from windows towards the top side of a small horizontal surface placed in different parts of
the room can be calculated. A condition for these calculations is that the radiation from the windows
is spread diffusely. Such is the case for windows with drapes or Venetian blinds as shown from previous
measurements. These measurements have also shown that a calculation of the distribution of light from a
window can be correctly performed only if room surfaces perpendicular to the window surface are divided
into sub-surfaces when angle and absorption factors are determined.
A. 2 Heat Balance Equations
Time variation of temperature in a room is calculated from the heat balance equations for the mate-
rial layers on the surface and in the walls and floors, for the interior side of the windows, and for
the room air.
Walls are considered to be divided into layers which are parallel to the wall surface. The equation
for a layer yields the magnitude of temperature change in a layer of thickness Ax during a time interval
of At (ordinarily 15-60 minutes) caused by the surface heat transfer of both of the limiting surfaces of
the layer.
Crank-Nicolson' s equation is used for an individual layer inside the wall in the form
K,9 , ^ + K„e ^ + K,e ^, , = K.e , + K,e + K,e (a)
1 n-l,t 2 n,t 3 n+l,t 4 n-1 5 n 6 n+1
where the temperatures at the beginning of the time period are written on the right side and the unknown
temperatures on the left side. The index n is used to denote the layer being treated while n-1 and n+1
are the adjacent layers.
If the three layers are of the same material, then K]^ = K3 = -1, K4 = Kfe = 1, K2 = 2 Ax2/a At + 2,
K5 = 2 Ax2/a At - 2. The constant a here denotes the material's thermal diffusivity.
Equation (A) is also used for the limiting surface between two different materials as well as the
surface of an air layer inside the wall. The coefficients then include the thicknesses, the thermal
conductivities and the thermal dif fusivities for the layers of material on both sides of the limit sur-
face, and, in the latter case, the thetnnal resistance of the air layer /3/.
The following relation is valid for a layer n at the surface of a wall:
-^^ll,t ^ ^2«n,t - Vr,t ~ ^^^.t =
= ^^nll * ^5^n * ^3^ * ^^4^ * ^6
The index nil indicates the adjacent layer, r the room air, and u a room surface from which long
wave radiation reaches the surface.
Equation (B) is applicable not only for surfaces of walls, floors and ceilings but also for the sur-
faces of heating units, interior sides of windows, and facade surfaces. Contrary to the K values of eq
(A), the F values of eq (B) are not all constant. The reason is that they include variables such as
radiation from windows and lamps, effect of heating units, shading coefficients, thermal resistances of
windows and the outside air temperature. For outdoor facade surfaces, Fg includes the sol-air tempera-
ture which contains the variables outside air temperature and radiation from sun and sky. It can be
pointed out that the equation for the sol-air temperature is so formed that the dependence of long wave
radiation upon the degree of cloudiness is taken into consideration at roof surfaces /lO/.
The convective surface heat transfer coefficient hj. for a room surface is dependent upon the tempera-
tures of the surface and air as given by the calculations. With each repeated application of the equa-
tions in which h^, appears, the most recently found value for h^ is inserted, during the calculation, in
the F coefficients.
Windows are assumed to lack thermal capacity. When eq (B) is used for the interior surface of a
window, the temperatures ^n*}.* ®n' ^u "h^*^^ ^'^^ valid at the beginning of the time interval At
are all set equal to zero, since the surface temperature at the end of the interval is then independent
of these temperatures.
A third type of heat balance equation, type (C) , is used for the room air. This equation states
that the heat which is introduced convectively from heating units in the room and by ventilating air and
possible leakage air is removed by the exhaust air and by convective surface heat transfer at the room
surfaces .
348
5. Calculation Procedure. Steps and Tolerances
The temperatures in the material layers, at the interior surfaces of windows, and of the room air
are all calculated simultaneously from a system of equations of the types (A), (B) , and (C) . The calcula-
tion begins with assumed values for these temperatures at time point 0 o'clock if a 24 h period is to be
studied, and then gives the temperatures after a first time interval of the calculation step's length At.
These temperatures, in their turn, make up the start values for the calculation of the temperatures at
the end of the following time interval of the same length. The same equation system as for the first
step is used here. However, the coefficients may have received new values. The calculation is continued
step by step until the variation for the whole calculation period has been found.
In general, the length of the period is 24 hours. It can however have other lengths, e.g. four times
as long. Stationary as well as non-periodic cases, where the start values are known and the input data
then varies at a known rate, can be studied.
Solution of the equation system which normally contains some fifty equations is done by relaxation.
A calculation referring to one and the same time point is repeated time after time with increasing accu-
racy. The difference between the two values for the same variable from two consecutive calculations are
compared each time with a predetermined tolerance, the relaxation tolerance. The calculations for the
time point in question continue until this difference is less than the tolerance for all variables. This
tolerance is dimensionless and is expressed in such a way that it can be used for temperature as well as
for air volumes and heating and cooling effects. ,
After the calculations have been carried out for all the time points during the period as determined
by At, they are repeated for the same time points during a new period. The difference between values for
one and the same variable at the end of this period and the previous period are compared with a predeter-
mined tolerance, the period tolerance. The calculations are now repeated for more periods until the
differences for all the variables fall below the prescribed tolerance. The same expression is used here
as for the relaxation tolerance. The value for the period tolerance must, however, be larger than that
for the relaxation tolerance.
The values of the calculated variables are printed out at time points determined by the print step.
The print out also includes the average values for the variables during the period. The pring step can
often be made longer than the calculation step which is determined by technical factors. The normal
value for the calculation step is 0.3 hours, for the print step 1 hour, for the relaxation tolerance
0.1 % and for the period tolerance 0.2 %. These values are used if no others are motivated.
6. Application Examples
6.1 The Effect of Wall and Floor Insulation upon Temperature Variation in a Room
During a series of clear days with equal sunshine and outside temperature, the mean room air tempera-
ture for a 24 h period is not dependent upon an exterior wall being insulated from the outside or inside.
If the room is surrounded by similar rooms with the same temperature, this mean air temperature is also
unaffected by the presence of a layer of insulation on interior walls and floors.
Both these measures, however, affect the magnitude of temperature fluctuation about the mean tempera-
ture. Heat storage in the structure has a dampening effect. Insulation of the heavier layers decreases
storage and results in stronger temperature fluctuation in the room. In this respect, insulation on the
inside of exterior walls produces the same effect as the insulation of interior structures.
For an illustration of this, consider the curves in figure 1 which are drawn on the basis of calcula-
tions using the computer program. These refer to a clear July day in Stockholm (latitude 59°21'N) for an
empty room without artificial lighting. The room was 2.7 m high and 5 m deep. It had a 3.8 m long window
wall and was ventilated over the whole daily cycle by 250 kg/h of outside air. The window had a glazed
area of 4 m2 with double glazing of ordinary window glass with light colored drapes on the inside, and
faced S 60° E. The temperature in the corridor was a constant 24°C.
The dash-dotted curves in the figure indicate a room having a reinforced concrete exterior wall in-
sulated on the outside with mineral wool. The floor is also of reinforced concrete and partition and
corridor walls are of cellular concrete. Dotted curves indicate a room with the ssuae exterior wall but
where the mineral wool insulation is located on the inside. The upper surface of the floor slab has been
covered by a wooden floor over mineral wool insulation, while the under surface has a suspended ceiling
with a thin layer of mineral wool insulation. The partition walls and corridor wall have also been in-
sulated with thin slabs of mineral wool mounted on studs. All wall insulation is protected by 1/2 inch
thick plaster board. The thickness of the concrete and cellular concrete has been decreased sufficiently
so that the weights of walls and floors including the insulation are the same.
349
In the second case described, the quality of sound insulation between the rooms has been improved,
but the the rmal conditions have deteriorated* Mean air temperature under a 24 h period for both cases
is 2A°C, but because of the insulation, the maximum temperature for the second case rises by 2.4° from
25.9° to 28. 30c. Mean temperature here during the period 8-17 o'clock rises by 1.6° from 25.7° to 27.3°C.
Figure 1 also shows how the mean temperature for the room surfaces varies during the period 8-17
o'clock. The value is a weighted mean value with the surfaces as weights (the floor surface temperature
is not included). Because of the insulation, the maximum value rises by 3.2° from 27.5° to 30.7°C, while
the mean value for the period 8-17 o'clock increases by 2.2° from 27.0°to 29.2°C.
The example shows that the weight of the interior walls and floors and the weight and thermal trans-
mittance of the exterior walls are not sufficient data on the building structure for calculation of the
temperature variation in rooms.
6.2 The Temperature Variation in a Room as Affected by Heat Gains in Adjacent Rooms and the Type of
Temperature Control (Individual or Central)
Given a building with several rooms of the same type along a facade and assume that a system is to
be installed for regulating the temperature of ventilating air in such a way that the room air tempera-
ture during working hours has a desired value independent of whether the room is being used or not. If
certain deviations from the desired value can be permitted, the problem is then to find out whether it
is necessary, under summer conditions, to provide controls in every room (individual temperature control),
or whether it is sufficient to feed cooled ventilating air of the same temperature to both unoccupied and
occupied rooms (central temperature control).
Figure 2 presents the results of calculations for similar rooms of the same size as in the preceding
example. Whereas the walls and floors were of a different construction, the window had the same orienta-
tion and incoming radiation is thus the same. Outside air temperature was also the same. The ventilat-
ing air was supplied at a rate of 300 kg/h during the whole 24 h period. It was cooled only during the
period 7-18 o'clock, and was 1°C warmer than the outside air during the rest of the time. Occupied rooms
were used by two persons during working hours (8-17), and lighting units were turned on during the after-
noon producing an effect of 25 W/m2 of floor surface. The windows in these rooms were double-glazed and
had roller blinds which were kept down except for during the afternoon; there were also drapes inside the
windows which were kept drawn during the whole 24 h period. The unoccupied room was assumed to be sur-
rounded by occupied rooms, and the blinds in this room were not used. The desired air temperature in the
rooms during working hours was 22°C. However, the ventilating air temperature was not allowed to fall
below 15°C.
Under these conditions, according to figure 2a, the air temperature in the occupied rooms can be
maintained at 22°C except for a slight increase in the afternoon. The ventilating air is then insuffi-
ciently cooled to wholly compensate for the heat release from people and lighting units.
Whereas the ventilating air to the occupied rooms need not be cooled so low as to 15° during the
morning, it is necessary for the ventilating air to the unoccupied room (see fig. 2b). This is based
upon the fact that the roller blinds between the panes in this room were not let down.
In cases of central temperature control where the ventilating air for the unoccupied room has the
same temperature as that for the occupied rooms the temperature during the morning and through the lunch
hour exceeds the desired value by ca. 1°. Contrary to this, the temperature towards the end of the work-
ing day is about 1.5° too low, as shown in figure 2c. On the basis of these deviations from the desired
value, it is possible to decide whether the cheaper alternative of central temperature control can be
accepted.
In the calculations for the unoccupied room the heat conduction through walls and floors between
this room and the occupied rooms was taken into consideration. This was accomplished by using the pre-
viously determined surface temperatures of the occupied rooms as the outside air temperatures at the
external surfaces of the walls and floors of the unoccupied room. These surfaces were treated as "fa-
cades" in the program. The surface heat transfer coefficient for them, were given a very high, fictive
value. This procedure involves approximations which, however, can be reduced by repeated calculations.
In this case, they proved to be insignificant.
Room air and ventilating air temperatures were considered as unknown quantities during the larger
part of the 24 h period in the calculations concerning the occupied room. Maximum values were then
assigned to them for a part of this period and minimum values for anotlier part. During the night, the
room air temperature was considered as the unknown.
During the calculations for the unoccupied room with individual temperature control,
minimum values were assigned to the temperatures of the room air and ventilating air
during the whole 24 h period. In the case of the central temperature control alternative
the room air temperature was treated as the unknown during the whole 24 h period.
350
7. References
HI Brown, G., Utilisation de calculateurs
electroniques pour resoudre les problemes
de transmission de la chaleur en regime
variable, Chauff.- Ventil.- Condition. 33
(), No. 10.
in Adamson, B., Brown, G., and Hovmoller, E.,
Dimensionerande utetemperatur . Statens
Byggnadsbesparingsutredning. Stockholm .
/3/ Brown, G., Metod for datamaskinberakning av
varme- och 1 jusstralning i rum och av kyl-
och varmebehov. Nat. Swedish Inst, for Build-
ing Res., Reprint 4, .
/4/ Antoni, N., Projekteringsunderlag for skol-
byggnader for grundskolan. Nat. Swedish Inst,
for Building Res., Report 50. Stockholm .
/5/ Lunelund, H., Varmestralning och Ijusstral-
ning i Finland. Svenska Tekniska Vetenskaps-
akademien i Finland, Acta 12. Helsingfors .
/6/ Brown, G. , and IsfSlt, E., Irradiation from sun
and sky in Sweden on clear days. Tables and
charts. Nat. Swedish Inst, for Building Res.,
Report 19. Stockholm .
PI Isfalt, E., A computer analysis of window shad-
ing coefficients by calculating optical and
thermal transmission. Contribution to this
symposium.
/8/ Kollmar, A., and Liese, W. , Die Strahlungsheiz-
ung. R. Oldenburg. Miinchen .
/9/ Squassi, F., Die Einstrahlzahlen in Wohnraumen.
Ges.- Ing. 78 (), No. 5/6.
/lO/ Hoglund, B. J., Mitalas, G. P., and Stephenson,
D. G. , Surface temperatures and heat fluxes for
flat roofs. Build. Sci. 2 (), No. 1.
Temperature, C
32
10 12 14 16 18 20 22 24 Time,hr
Mean temperature
of room surfaces
Room air
" temperature
Outdoor air
temperature
Radiation through
unshaded window
1. Calculated temperature of air and room surfaces in two rooms whose walls and floors have the same
weight but different insulation:
Exterior wall insulated on the outside,
non-insulated interior walls and floors
Exterior wall insulated on the inside,
insulated interior walls and floors
351
Temperature, °C
12 1 , . . . ■ . . . . , . 1
0 2 4 6 8 10 12 14 16 18 20 22 24
Tempera fure , °C
0 2 4 6 8 10 12 14 16 IS 20 22 24
I ernperoture , (_
24
22
20
18
16
14
12
0 2 4 6 8 10 12 14 16 18 20 22 24
Room air temperature
VenKlaling air temperature
2. Calculated air temperatures in occupied and unoccupied rooms.
a. Occupied room
b. Unoccupied room, individual control
c. Unoccupied room, central control
352
Optimization of an Air-Supply Duct System
W. F. Stoecker , R. C. Winn , and C. 0. Pedersen
Department of Mechanical and Industrial Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois
The design of a multi-branch air supply system is complex because there are
as many decisions to make as there are sizes of duct sections to specify. A fur-
ther complication is that a decision on the size of one section affects the per-
formance of the entire system. If an optimal duct system is sought, then, the
design process becomes a multi-variable optimization.
The premise on which the mathematics of the procedure explained in this
paper is based is that all of the available static pressure is dissipated in the
duct and fittings with no artificial pressure drop due to dampers. Furthermore,
of the multitude of systems that would be balanced without the addition of damp-
ers, the computer program selects the one with minimum cost.
The objective function is the total cost of the system based on a fixed
cost per pound of metal. The constraints appear because the pressure drop from
the fan discharge to each outlet must equal the available static pressure.
Thus, there are as many constraints as outlets. The forms of both the objective
function and the equality constraints are preditable, so the optimization yields
itself to the method of Lagrange multipliers.
This paper presents the basis of a computer program which performs this op-
timization for a circular-duct system. The user of the program provides the fol-
lowing information:
(a) available static pressure at the fan outlet,
(b) the geometrical coordinates of each outlet, branch, and elbow,
(c) the flow rate at each outlet, and
(d) the cost of the metal per pound.
The printout includes the diameter, duct surface area, velocity, pressure drop,
and cost for each section of duct for the optimum system.
Key Words: Air supply, duct system, optimization.
1. Introduction
An air-supply system is a requirement for practically every environmental control unit for a build-
ing. The design of the supply system is a complex one because the system has many components — each
section of straight duct and each fitting is a component — and as is true of classical systems, component
performance is interrelated. The question might be raised, "How can such a complex system be designed
and constructed in practice by methods that are usually unsophisticated?" There are two answers
(a) The most popular design procedures afford a systematic way of arriving at a workable system, and
Professor of Mechanical Engineering.
Research Assistant, presently with U.S. Air Force at Columbus, Mississippi.
Assistant Professor of Mechanical Engineering.
353
(b) Most duct systems are not optimum.
The two answers are > related. The first task of the designer is to specify a system that will meet
the requirements, which for duct systems is to provide the specified flow rate at designated locations.
Furthermore, the designer must perform his task relatively quickly — he cannot make a career of one or
two duct systems. To his aid come the standard procedures for duct design, such as the "velocity-
reduction method" and the "equal-friction method." The merits of these methods are
(a) that they result in workable systems, and
(b) that they provide methodical procedures for the designer to follow which simplify his task.
A further merit of the velocity reduction method is that it provides velocity limits which acknowledge
noise considerations. The equal-friction method, on the other hand, while it has no built-in procedures
for limiting velocities does come closer to achieving a duct system of minimum first cost.
One of the coverups for a non-optimum design is a high fan static pressure. Given an unlimited
static pressure at the fan and a generous supply of dampers , almost any duct system will provide the re-
quired flow at designated locations. Unfortunately, the economies realized in reduced design time are
sometimes dwarfed by unnecessarily high first and operating costs.
This paper presents the basis for a procedure for optimizing the first cost of an air-supply system.
The procedure has been incorporated into an operating computer program. Specifically, the optimization
problem can be formulated as an objective function with equality constraints which is soluble by the me-
thod of Lagrange multipliers. The computer program executes the optimization, solving the set of non-
linear simultaneous algebraic equations by the Newton-Raphson technique.
2. Air-Supply System
A sample duct system (shown schematically in fig. 1) must supply Qj , Qj i , and Qj j j cfm, respective-
ly, at the positions shown. The optimization procedure presented in this paper determines the minimum-
cost duct system for a given available static pressure at point 1. The minimum cost system is the one
which requires the minimum weight of metal, a proposition which conforms to the conventional method used
by contractors in making bid estimates.
An immediate question that emerges is whether the total system can truly be optimum if the static
pressure at point 1 is arbitrarily assigned. Figiire 2 shows that when the static pressure is extremely
low, the duct cost will be excessive due to its large size regardless of the design procedure used. On
the other hand, when a high static pressure is selected, the lifetime operating cost becomes the control-
ling quantity. There is a certain static pressure that results in minimum lifetime cost. For any
static pressure there will be a minimum cost duct system. The program described in this paper designs
such a system. To obtain the information required to construct figure 2, this program must be used to
find the optimum duct system pressures.
3. Premise of Optimum Design
From physical reasoning the optimum duct system is one where the available static pressure is dis-
siptated completely in each run. A "run" is defined as the path from the fan discharge to an air outlet.
The basis for this premise is that if a run should exist where the flow is too high, the flow should be
reduced not by throttling with a damper, but by reducing the size and thus the cost of some duct section
in that run. The consequence of applying this premise is that the resulting duct system uses all of the
available static pressure to overcome friction in the straight ducts and fittings, and no static pres-
sure is dissipated in dampers.
Obedience to the foregoing premise, however, does not describe a unique duct system. This fact
could be shown schematically as in figure 3. Assume that the ducts shown by solid lines are of such
size that they deliver the desired flow rates of air to the two outlets when a certain static pressure
exists at the fan outlet. Another duct system tha^ has a smaller size trunk section and larger size in
the branches and will also deliver the desired flow rates can be found (shown by the dashed lines).
One of those two duct systems undoubtedly will have a lower cost than the other. A conclusion, then, is
that there is an infinite nximber of duct systems that consume the available static pressure, but only
one of these will have minimized cost.
4. Cost Function
The mathematical form of the duct optimization problem consists of two parts:
(a) the cost function which is the objective function to be optimized, and
35A
(b) the constraints.
For circular ducts the cost of a section is
Cost of section = ttDLWCCCP) (1)
where
D = diameter of the duct, ft
L = length, ft
W = effective weight per square foot of duct surface (includes allowance
for fittings, seams, hangers, and scrap), (lb)(ft)~^
CCP = cost per pound of duct, (dollars) (lb) '
The allowance for fittings, seams, hangers and scrap in W is 20 percent of the weight of duct surface.
The weight of the duct per ft^ conforms to recommended construction for low-pressure ductwork (less than
2 in. of water static pressure) as recommended in Tables 11 and 15, Chapter 3 [1]'*. The gauge of the
metal is thus a function of the duct -diameter. The total cost, COST, of the example system in figure 1
is
COST =CtCtC+C+C+C+C (2)
^ 1-2 3-4 S-6 4-5 6-7 S- 9 ^10-11 ^
When the costs of each section from eq (1) are substituted into eq (2), the variables for optimization
become the diameters. The other terms L, W, and CCP are dictated by costs and layout and are not vari-
ables of optimization.
Rather than choosing the diameters as the variables, it is more convenient for later manipulations
to express the diameter in terms of a pressure drop, Ap. The pressure drop in a section of straight
duct can be expressed by
2 p
Ap = 12f ^^-f (3)
where
Ap = pressure drop, in. of water
f = friction factor dimensionless
V = velocity, fps
-1 -2
g = gravitational constant 32.2 (ft)(lb )(lb ) (sec)
c ml
_3
= density of air, (lb) (ft)
_3
p = density of water, (lb) (ft)
Further, the velocity V can be expressed
60(t7D^/i+)
(4)
4 .
Figures m brackets indicate the literature references at the end of this paper.
355
where
Q = flow rate , cfm
Substituting eq (4) into eq (3) and solving for D results in
0. 2
D = constant/Ap (5)
Substituting eq (5) into eq (1) and then into eq (2) results in the objective function which is the
total cost,
■ , - K K K K
^^r--. 1-2 3-4 5-6 4-5
COST = — - t — - + — — - +
(^Pl-2^ ^^P3-4^ (^P5-6^ (^P4-5^
K K„ „ K
I I I 10-11
2
The constants K incorporate the length, flow rate, friction factor and effective weight per ft for each
section .
Equation (5) is the function that must be optimized subject to the constraints that will be pre-
sented in the next section.
5. Constraints
The constraints essentially state that all of the available static pressure will be dissipated in
friction in the fittings and straight sections. The number of constraints is the same as the number of
runs which also equals the number of outlets. The constraint equations for the system in figure 1 are:
APj., + Ap^ + Ap^ + Ap^_^ + Ap^_^ + Ap^_^ + Ap^_^ + Ap, = SP (7)
+ ^Pf ^ ^Pc + ^P2-4 + ^P4-5 + ^P5-6 + ^^6-7 + ^Pn = (8)
APl-2 + ^Pf + ^Pc + ^P2-4 + ^P4-5 + ^P5-8 + ^P8-9 + ^P9-10 + ^PlO-11 + ^PlII = O)
where
Ap^ = pressure drop in filter, in. of water
Ap = pressure drop in coil, in. of water
c
APj = pressure drop in terminal at outlet I
SP = static pressure at the fan, in. of water
The optimization procedures consist of minimizing eq (6) subject to the constraints of eqs (7-9).
6. Lagrange Multiplier Solution
The objective function, eq (6), and the constraints, eqs (7-9), are soluble by the method of
Lagrange multipliers. If an objective function y is to be minimized, where
356
y = y(Xj .•••><„)
subject to the constraints
0 (x -•••X ) = 0
ml n
the method of Lagrange multipliers [2] states that the optimum occurs where the following equations are
satisfied:
Vy - A V(j) - ••• - X V(J) = 0 (10)
^11 mm
where
_ 3y -:- 3y — 3y —
dX, 1 dX^ 2 dx n
1 2 n
and are constants called Lagrange multipliers.
Equation (10) is a vector equation and in order for it to equal zero the coefficients of each unit
vector, such as ij must equal zero. Equation (10), therefore, represents n scalar equations which,
along with the m constraints, is a system of equations for the n + m unknowns, namely, x , •••x ,
1 m
Solving the equations represented by the vector equation, eq (10), along with the constraint equa-
tions poses special requirements because the equations are often nonlinear. An iterative method for
solving nonlinear simultaneous equations is the Newton-Raphson iteration [2]. In this process, trial
values are assumed for each of the unknowns. These trial values are substituted into the n + m equa-
tions. If all of the equations are satisfied the problem is solved. Usually, however, the equations
will not be satisfied with the first trials and the values of the variables need to be corrected. To
determine how much each of the trial values should be changed, the Newton-Raphson technique prescribes
a set of simultaneous linear equations . The solution of these linear equations gives the corrections
which must be applied to the previous trial values to provide more correct values of the variables.
The fortunate circumstance which makes the method of Lagrange multipliers so applicable to the duct
optimization problem is that the form of eqs (6-9) is dependable — the objective function is a sum of
terms, all of which have the same form, and the constraints are linear in the variables which are to be
optimized, Apj . After the optimal values of the Ap's have been determined, the optimal diameters for
each section can be computed.
7. Computer Program
Robert C. Winn [3] developed a computer program to optimize duct systems automating the foregoing
mathematical procedure. The listing, flow diagram, and documentation of this program are found in [3].
To anticipate the eventual use of this program under coordinate geometry, the duct system is described
in terms of the coordinates of all elbows, branches and outlets. Once this information is entered, the
computer determines the angle of turn of an elbow or branch. The complete list of input information re-
quired is :
(a) static pressure developed by the fan,
(b) type of each joint and its geometrical coordinates,
(c) pressure drop through filters, coils and outlets,
(d) upstream and downstream joint numbers of each outlet,
(e) air flow rate at each outlet,
(f) temperature of the air at the fan, and
357
(g) current cost of ductwork per pound.
The output, as example of which is shown in figure 4-, consists of the following information for
each section: diameter, velocity, flow rate, length, duct surface area, sheet metal gauge, pressure
drop, and cost. In addition, the total cost of the entire duct system is provided. The output corres-
ponds to the duct system shown in figure 5 .
8. Strengths and Limitations of the Program
While the application of a standard mathematical tool and the computer program in which it is
utilized are intended to be a contribution to improved procedures in the design of environmental systems,
the work is not to be considered complete. One of the obvious extensions would be to include the capa-
bility to optimize a system of rectangular duct in addition to circular duct which the program now can
accommodate. It would be realistic to encounter a dimensional limitation, such as the depth of the duct,
and in such a case the program would determine the optimum width within this depth limitation.
The method for calculating cost used in this program multiplies the weight of metal by a factor.
This practice oversimplifies the influences which contribute to the cost since the weight of metal alone
is not an accurate indicator of, for example, the labor cost. On the other hand, the most commonly used
method of estimating the cost of a duct system for bidding purposes is first to evaluate the weight of
metal and then multiply by a factor which varies somewhat depending upon the number and type of fittings
and ease or difficulty of installations. As long as bids are determined on this basis, the weight of
metal is the preferred quantity to minimize.
In its present status the program imposes no limits on velocity. In other words, a short run of
ductwork with the outlet close to the fan will optimize at an extremely small diameter because all of
the available pressure must be dissipated in the duct itself. Standard practice calls for enlarging the
duct and installing a damper to accomplish the pressure drop. It should not be difficult to incorporate
in the computer program the provision for checking the velocity against some prescribed maximum, enlarg-
ing the duct if necessary to abide by the velocity restriction, and including on the output a statement
that dampering will be needed. Such a refinement of the program is planned. This practice, however,
raises a more basic question. Since the limitation of velocity is particularly to reduce the noise
level, which process would generate the most noise for a given drop in pressure, flow through a damper
or flow in a length of small diameter duct? There is evidence that a detached boundary layer (as in
flow past a damper) generates more noise than an attached boundary layer (as in flow through a small
duct). A more thorough study of this question seems warranted.
The pressure drop through branch takeoffs and the straight-through portion of branch are computed
using data from [1]. The graphical data have been converted to equation form for convenience in the
computer program. In air-duct systems the pressure drops in fittings will be of the same order of mag-
nitude as that experienced in the straight sections of duct so accuracy in the fitting calculation is
important. The calculation of pressure drops in straight sections is probably reliable, but the pre-
diction of pressure drops in fittings is highly dependent upon the quality of craftsmanship of the fit-
ting. The use of fittings manufactured in factories under controlled conditions and carefully tested
will add to the reliability of optimization efforts such as this.
The principal claim made for this method of duct design is that it results in the duct system of
minimum first cost for a specified available static pressure. A further benefit is that it results in
a balanced system. No one would be so foolhardy as to install a system designed with this computer pro-
gram and omit dampers in each branch. The accuracy of the basic pressure drop data and the quality of
workmanship is just too variable. It is likely, however, that the system will be more nearly balanced
than systems designed by other methods, so that the cost of balancing should be reduced.
9. Acknowledgments
During his graduate studies the work of R. C. Winn on this project was supported by an Industrial
Research Assistantship of Skidmore, Owings and Merrill.
10. References
[1] American Society of Heating, Refrigeration and [3]
Air Conditioning Engineers, ASHRAE Guide and
Data Book , Systems and Equipment Volume , New
York, .
[2] Stoecker, W. F. , "Design of Thermal Systems,"
McGraw-Hill Book Co., New York, (in press).
Winn, R. C, "Development of a Computer Pro-
gram for the Optimum Design of Air Supply
Duct Systems," M.S. Thesis, University of
Illinois at Urbana-Champaign , Urbana, Illinois
.
358
0
Fan
Filter Coil
4-
2 3-
4
7
Q
E
cfm
cfm
5 8
-10
-11
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IE cfm
Figure 1. A multiple-branch duct system.
Figure 2. Effect of fan static pressure on lifetime
cost of combined fan and duct system.
359
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It is recognized that many organizations have in their computer program library a
method for solving Colebrook's equation and calculating the pressure drops of fluids in
a pipe. Nevertheless, this paper is being presented for those who wish to initiate
modeling of duct and piping systems to meet their needs. The only limitation to model-
ing various types of systems is the fittings in your program library. More effort
needs to be expended in the correlation of fitting data. To assist in the correlation
of data. Dr. Inoue has an excellent summary of fitting data in his "Duct Design Hand-
book"(4).
In addition to presenting the program listings for determining friction factors
and calculating the pressure drop in a pipe the pertinent subroutines for calculating
the properties of moist air are presented for your convenience. Also Illustrated in
section 3 Is a friction chart for air at a density of O.062 lbs-ft"3, which Is equiva-
lent to an altitude of feet.
2. Pressure Drop Calculations
2.1 Friction Factors
Of the numerical techniques analyzed to solve Colebrook's equation it was found
that the Newton-Raphson method requires the least computer execution time. This sec-
tion presents an analysis of this method for solving the friction factor equation.
Rearranging eq (1) and setting the function of the friction factor, F(f), equal to
zero yields eq (2). For fixed values of Reynolds number (Rj^j), material roughness
factor (E), and pipe diameter (D), the value of P(f) can be calculated for incremental
values of friction factors (f) and the results plotted as Illustrated in figure 2. In
Fffl
+ 2 log
10
12 E
2.51
= 0
(2)
this example Reynolds
600,000 and 0.001, re
numerical solution on
Initiated by assuming
are unlikely since th
At the Initial value
lated by eq (2) . Aft
the Intercept to the
f (0.) In the sec
the Intercept to the
point the difference
number and the dlmensionless ratio E/d (relative roughness) are
spectively. The methodology is best illustrated by following the
this specific graphing of the function. The iteration process is
0.01 as a value for the friction factor f. Values less than 0.01
e Reynolds number would have to exceed 2.5 x 10° (refer to fig 1).
of f (0.01) the value of the function, F(f), is 2,988 as calcu-
er calculating the derivative of function by eq (3), the value of
f-axis is calculated by eq (4) to be 0.- Using this value of
ond iteration process the value of P(f) is 0,892, and the value of
f-axls of a line tangent to the curve at O.892 Is 0.019^. At this
between the last two values of f is 0.- This difference is
F(f)
2 f
1/2
1 +
12 E
0,
2.51
(3)
■NEW
= f
OLD
LF'(f) J
greater than the desired accuracy of 1/2 percent or difference of 0.001, therefore the
iteration process continues and f is reset to 0.019^- Using this value of f in the
next iteration the value of the next intercept to the f-axls is 0.. Since the dif-
ference between this value (0.) and the previously calculated value of f (0,019^)
is 0,, which is less than the difference desired, the iteration process is termi-
nated. The solution for the friction factor, therefore, is 0,. By referring to
364
figure 1 the correlation of Colebrook's equation to Moody's diagram is readily demon-
strated. To calculatb a friction factor three iterations are usually required, however
in a few cases, four iterations will be necessary to yield a solution. A listing of
the computer program for calculating friction factors is presented in figure 3. Figure
4 is a flowchart for this program.
2,2 Pressure Drop in Straight Ducts
The pressure drop in a pipe may be calculated by the Darcey-Wlesbach eq (5). This
relationship, used with the expression for velocity pressure (eq 6), may be used di-
rectly In your mainline programs, or as a subroutine. A Fortran listing of the pres-
sure drop subroutine, naimed DUCT, is presented along with the friction factor subrou-
tine (PRICT) in figure 3. These programs, in addition to your modeling programs, may
be readily used to develop friction charts for any fluid, fluid density and viscosity.
AP = f [§] (5)
where :
Z\P =
pressure drop. Inches water gage pressure (iwgp)
f
friction factor, dimensionless
L
pipe length, inches
D
pipe diameter. Inches
Hv =
velocity pressure, iwgp
/O
fluid density, lbs-ft"3
V
fluid velocity, ft-min"'''
2.3 Properties of Moist Air
To use the friction factor and pressure drop programs, the density and viscosity
of the fluid must be known. For your convenience in modeling air duct systems, or
generating other air friction charts (see section 3)> the pertinent moist air subrou-
tines are presented in the following sections.
a. Barometric Pressure
Altitude and barometric data by NACA (5) was correlated linearly by the method of
least squares between sea level and feet elevation. The resulting relationship,
eq (7), has a coefficient of determination of 0.999. Refer to figure 5 for the func-
tion subroutine of this equation.
BP = 29.841 - (0.) (10"3) (ELEV) (7)
where :
BP = barometric pressure. Inches mercury
ELEV = altitude, feet
b. Moist Air Density
Function subroutines for the properties of moist air are presented in figure 5 and
are based on the "Algorithms For Psychrometric Calculations" by the National Bureau of
Standards (6). As may be noted the subroutine for calculating the air density (RHO) in
turn calls the absolute humidity (W), the partial pressure of water vapor (PV), and the
partial pressure of water vapor in moisture saturated air (PVS) subroutines.
365
c. Viscosity of Moist Air
Temperature-viscosity data for dry air at l4.7 psi from Jakob (7) is approximately
linear, and therefore the data was fitted by the least squares method to the regression
line between -60°F and +300°F. The resulting eq (8) has a coefficient of determination
of 0.991.
p. = 0.039^8 + (6.213) (10"5)T (8)
where :
p. = dynamic viscosity, lbs mass-f t~-'--hr~"''
T = dry-bulb temperature, °F
Since the viscosity of moist air varies little from that of dry air at normal
atmospheric pressure (8), the above equation for viscosity is used to calculate the
Reynolds number of air flowing through the duct. The function subroutine for viscosity
is presented in figure 5-
3. -Foot Friction Chart
An air friction chart for an altitude of feet using the subroutines in this
paper is presented in figure 6. Comparing these values to the standard air friction
chart in the ASHRAE Guide (9) the pressure drop for the less dense air at the higher
elevation ranges from 20 to 32 percent less than that at sea level (^=0.075 lbs-ft~3).
For example, for a flow of cubic feet of air per minute the loss in 100 feet of
6-lnch diameter pipe at sea level is 6.9 inches of water (refer to fig 6), while at
feet ^=0.062) the loss is 5-5 inches of water. This decrease in air density re-
sults in a 20,3 percent (based on standard air) reduction in resistance to air flow. As
stated previously, other charts can be readily generated by developing a mainline pro-
gram utilizing the friction factor (FRICT) and pressure drop (DUCT) subroutines.
4. Re
(1) L. F. Moody, "Friction Factors for
Pipe Flow", ASME Transactions, Vol. 66,
, p. 671.
(2) C, F. Colebrook, "Turbulent Plow in
Pipes, with Particular Reference to
the Transition Region between the
Smooth and Rough Pipe Laws", Jour.
Inst, Civil Engrs, London, Feb. ^
p. 133.
(3) J. K. Vennard, "Elementary Fluid Mech-
anics", 3i'd Edition, Wiley, New York,
. p. 193.
(4) U. Inoue, "Duct Design Handbook",
Waseda University, Japan, pp. I16-I37.
(5) "Tables and Data for Altitudes to
65,800 Feet", NACA Report , Wash-
ington, D.C., , pp. 66-81.
(6) T. Kusuda, "Algorithms for Psychromet-
ric Calculations", National Bureau of
Standards, U.S. Department of Commerce,
Washington, D.C., Report No. ,
March, .
rences
(7) M. Jakob and G. A. Hawkins, "Elements
of Heat Transfer", 3rd Edition, Wiley,
New York, , p. 10.
(8) "Handbook of Fundamentals", American
Society of Heating, Refrigerating and
Air-Conditloning Engineers (ASHRAE),
New York, I967, figure 12, p. 109.
(9) "Guide and Data Book, Equipment",
ASHRAE, New York, I969, figs 2 & 3,
pp. 26-27.
366
Figure 1, Moody Diagram (from ref 8, p. 87, fig 12)
367
JO saniBA
368
C NOMENCLATURE:
C E IS THE PIPE MATERIAL ROUGHNESS FACTOR, FEET (SEE REF. 8, P. 88, TABLE 4)
C DIA IS THE DIAMETER OF THE PIPE, INCHES
C CFM IS THE VOLUMETRIC RATE OF FLUID FLOW, CUBIC FEET PER MINUTE
C RHO IS THE DENSITY OF THE FLUID, LBS PER CUBIC FEET
C AMU IS THE VISCOSITY OF THE FLUID, LBS PER FT-HR
C ALGT IS THE LENGTH OF PIPE, FEET
C FRICT IS THE FRICTION FACTOR, DIMENSIONLESS
C DUCT IS THE PRESSURE FOR THE LENGTH OF PIPE (ALGT) INPUTED, INCHES OF WATER
C FRICTION FACTOR (FRICT) FUNCTION SUBROUTINE
FUNCTION FRICT(E,DIA,CFM,RHO,AMU)
RENNO= ( 916 . 733*RHO*CFM )/( AMU*DIA )
F=0.01
10 C1=12.*E/(3.7*DIA)
C2=SQRT(F)
C3=2.51/(RENN0*C2)
c5=ci+c3
FF-1 . 0/C2+0 . 9* ALOG ( C4 )
FDF= ( -0 . 5/( C 2*F ) ) * ( 1 . + ( 2 . l801/( C4*RENN0 ) ) )
FNEl^=F-(FF/FDF)
DIF=ABS(FNEW-F)
IF(DIF-0.001)30,30,20
20 F=FNEW
GO TO 10
30 FRICT=FNEW
RETURN
END
C PRESSURE DROP (DUCT) FUNCTION SUBROUTINE
FUNCTION DUCT ( DIA , ALGT, CFM, RHO , FRICT )
VP=RHO* ( CFM*0 . /DIA**2) **2
DUCT=PRICT* ALGT* VP*12. /DIA
RETURN
END
Figure 3, Subroutine Listings for Calculating
Friction Factors and Pressure Drop
369
ENTER
SUBROUTINE
CALCULATE
REYNOLDS •
NUMBER
ASSUME INITIAL
VALUE OF
FRICTION FACTOR
(f ) TO BE 0.01
FSNIO
-<
CALCULA'j
OF COLI
EQUATIOI
(see Nc
l?E VALUE
:brook
J, F(f)
)te 1)
NOTES ;
(1) F(f) = ^ + 2 log^o
(2) F'(f) = - _1
2f / f
1 +
12-i<-E + ^.5
D*3.7
0,
^NEW - f -
F(f)
F'(f)
(h) FSNlO, FSN20, FSN30 are
Fortran Statement Numbers, see listing, figure 3
CALCULATE VALUE
OF DERIVITIVE
OP THE FUNCTION,
F'(f)(see Note 2)
CALCULATE NEW
VALUE OF (f )
BY NEWTON-RAPHSON
METHOD(see Note 3)
CALCULATE ABSOLUTE
VALUE OF THE
DIFFERENCE
FSN20 I
SET (f)
EQUAL TO
LAST VALUE
CALCULATED
SET FRICT
EQUAL TO LATEST
VALUE CALCULATED
RETURN TO
CALLING
PROGRAM
Figure 4. Flowchart of the Friction Factor Program
370
c
c
c
c
NOMENCLATURE:
DBT IS THE DRY-BULB TEMPERATURE, DEGREES F
WBT IS THE WET-BULB TEMPERATURE, DEGREES F
ELEV IS THE ALTITUDE ABOVE SEA LEVEL, FEET
C DENSITY OF MOIST AIR (RHO), POUNDS PER CUBIC FOOT OF DRY AIR
FUNCTION RHO( DBT, WBT, ELEV)
V0L=(0.75^*(DBT+459.688)*(1. +. *(W(DBT, WBT, ELEV)/436o. ) ) )/BP
l(ELEV)
RH0=1./V0L
RETURN
END
C BAROMETRIC PRESSURE AS A FUNCTION OF ALTITUDE (BP), INCHES MERCURY
FUNCTION BP (ELEV)
BP= ( 0 . 11E02 ) - ( 0 . E-O3 ) *ELEV
RETURN
END
C HUMIDITY RATIO OF MOIST AIR (W), LBS OF WATER VAPOR PER POUND OF DRY AIR
FUNCTION W( DBT, WBT, ELEV)
W=0 . 622* ( PV( DBT, WBT, ELEV)/( BP ( ELEV) -PV(DBT, WBT, ELEV) ) )
IF(W)10,20,20
10 W=0.
20 RETURN
END
C PARTIAL PRESSURE OF WATER VAPOR IN MOIST AIR (PV), INCHES MERCURY
FUNCTION PV( DBT, WBT, ELEV)
PV=PVS(WBT)-(0.*BP(ELEV)»(DBT-WBT)*(l.+(WBT-32. )/l571. ) )
IF(PV)10,20,20
C PARTIAL PRESSURE OF WATER VAPOR IN MOISTURE SATURATED AIR (PVS), INCHES MERCURY
FUNCTION PVS (TEMP)
DIMENSION A(6),B(4)
DATA A/-7 . , 5. , -1 . 38I6E-7, 11 . 344, 8 . I328E-3, -3 . /
DATA B/-9 . , -3 . , 0 . , 0 . /
T=(TEMP+459.688)/1.8
IF( T-273 . 16 ) 10, 20, 20
10 Z=273.l6/T
P1=B( 1)*(Z-1. )
P2=b(2)*0.*AL0G(Z)
P3=B(3)*(1.-1./Z)
p4=0.*ALOG(B(4) )
GO TO 30
20 Z=373.l6/T
P1=A( 1)*(Z-1. )
P2=a(2)*0.*AL0G(Z)
P3=A 3 *(10**(A(4)*(1,-1./Z))-1.)
p4=a(5)*(io**(a 6)*(z-i.))-i.)
30 PVS=29.921*10**(P1+P2+P3+p4)
RETURN
END
C VISCOSITY OF MOIST AIR (AMU), LBS MASS PER FT-HR
FUNCTION AMU (DBT)
AMU=0 . +0 . E-4*DBT
RETURN
END
10 PV=0.
20 RETURN
END
Figure 5.
Subroutine Listings for Determining
the Properties of Moist Air
371
®
0)
-p
3
a
0)
.02
,0U .06 .1 .2 .k .6 1. 2.
Friction Loss in Inches of Water per 100 ft
k. 6.
10.
Figure 6, Friction of Air at an
Altitude of Feet
372
Friction Loss in Inches of Water per 100 ft
Figure 6. (cont'd) Friction of Air at an
Altitude of Feet
373
Pressure Loss Coefficients
for the
45-Degree Return Air Tee
H. P. Behls and W. K. Brown, Jr.
Sargent & Lundy, Engineers
Chicago, Illinois
For good design of duct system, the losses of the corn-
components In the system network must be known. For the tee
there exists an Infinite number of combinations of through-
flow and branch loss coefficients. Data for both the
through and branch coefficients have been correlated for
the 45-degree return air tee and the resulting family of
curves presented. For those who wish to develop their own
computer programs, the subprogram listings are provided.
In addition, the significance of the negative loss coeffi-
cients is discussed.
Key Words: Computer, design, exhaust, loss coef-
ficients, pressure drop, return air, tee.
1. Introduction
The tee is the focal point in any duct system analysis because the resistance of
the main duct network, including the losses in the through portion of the tee, should
match at design air quantities the resistance of the branch network; otherwise the
system will not be in balance. Heretofore little emphasis was placed on the losses
which occur concurrently through both the main and branch sections of tees. For both
good design practice and modeling of duct systems on the computer the losses occurring
at the same time must be known. This paper presents the correlation of experimental
data for the 45-degree return air tee which has a circular cross-section, equal inlet
and outlet areas in the main, and a branch area equal to or less than the main. For
those who wish to develop their own duct system models for computer design, the pro-
gram listings for the tee-through and tee-branch loss coefficients are Included herein,
2. Tee Loss Coefficients
Forty-five degree return air through-flow and branch to main loss coefficients
have been determined experimentally by Petermann( 1) 1 and the coefficients summarized
by Dr. Inoue in his handbook for duct design (2) as presented in table 1.
Although this discussion pertains to the data correlation of the 45-degree tee
with a round cross-section, other data are available, primarily the 90-degree return
air tee (3j 4), and the supply air tees listed in table 2. These data should also be
correlated so that more diversified duct systems may be modeled.
2,1 Tee-Through Flow Loss Coefficients
Petermann's tee-through loss coefficients are best represented (least standard
deviation from the original data) by a family of parabolas as shown in figure 1. As
Figures in parenthesis indicate the literature references at the end of this
paper.
375
Table 1. 45-Degree Return Air Tee Loss Coefficients
Tee Configuration
Flow Path
Loss Coefficient (A)
Main
Area
Ratio
(D/B)
Velocity Ratio (U/D)
0.2
0.4
O.b
O.B
1.0
1.0
-0.17
0.06
0.19
0.17
0.04
3.0
-1.50
-0.70
-0.20
0.10
0
8.2
-5.70
-2,90
-1.10
-0.10
0
Branch
Area
Ratio
(D/B)
Velocity Ratio (B/D)
0.4
0.6
O.B
1.0
1.2
1.0
0
0.22
0.37
0.37
0.20
3.0
-0.36
-0.10
0.15
0.40
0.75
8.2
-0.56
-0,32
-0.05
0.24
0.55
Table 2. Sources of Tee Data
Angle
Type of Take-off
Author
Reference
450
Straight
Petermann
(1)
90°
Straight
Ashley
(5)
90°
Conical
Ashley
(5)
illustrated below, these parabolas can be correlated to the zero coordinates since the
location of their apexes is related to area ratio. This correlation is a straight
line going through the point (1.0, 0.0) with the area ratio approaching Infinity as
the velocity ratio approaches 1.0. The resulting equations for the displacement of
the apexes from the (1.0, 0.0) coordinates are as follows:
376
H'(HPRIM) = 0. (^^^
YK = 0, - 0. H (2)
where :
H = 1.0 - H'
ARDB = area ratio from the tee main to the
tee branch, dimenslonless
HPRIM = acronym used In computer program
The family of parabolas at the (0.0, 0.0) axis are represented by eq (3). It
should be noted that the parabolas approach the negative Y-axis as the area ratio
approaches infinity.
COEP = [-1.461 ARDB°-j ^2 (3)
where :
T = H - VRUD
VRUD = velocity ratio from upstream of the
tee main to downstream of the tee main,
dimenslonless
With the equation of the parabolas and their displacement known, the tee-through
loss coefficients can be readily calculated by eq (4). Using these relationships, the
data may be represented as shown in figure 2, or calculated utilizing the computer
listing presented in figure 3- For comparison purposes the parabolas for area ratios
of 1.0, 3-0 and 8,2 are superimposed on figure 1 to show the correlation to Petermannfe
original data. The coefficient of correlation of the curves to the original data is
0.987
Am (TEETH) = COEF + YK (4)
where :
Ajy] = main loss coefficient, dimenslonless
TEETH = acronym used in computer program
2.2 Tee-Branch Plow Loss Coefficients
Along with data by Brown (6), Pettermann's tee-branch coefficients are shown in
figure 4. Since both sources of data correlate exceptionally well, confidence in the
data is high and Petermann's data was fitted to the general form of [Ag + 1 = VR2]
as suggested by Healy (7). The resulting correlation, with a coefficient or correla-
tion of 0.962, is given by eq (6), and using this relationship the family of curves
in figure 5 were generated. It should be noted that as the area ratio increases the
loss coefficient approaches the ideal loss coefficient given by |^A-g +1 = VR^].
1 =
" 1.'
"0, (VRBD)'
+
_ VARDB.
L VARDB J
[VRBD^-Oj
(5)
where :
Ag = branch loss coefficient, dimenslonless
ARDB = area ratio from the tee main to the tee
branch, dimenslonless
VRBD = velocity ratio from the branch to
downstream of the tee main, dimenslonless
377
Figure 5 can be readily utilized by those who have a need for expedient data. For
those who wish to simulate and design their systems by use of the computer the program
listing for determining the branch loss coefficients is presented in figure 6,
2.3 Total Pressure Drop
With the loss coefficient known the total pressure loss in the through or branch
portions of the tee may then be calculated by the following expression.
AP = A[Vj/]^^ (6)
where:
AP = main or branch total pressure drop,
inches of water gage
Vj) = downstream velocity, feet-min"-'-
lO = moist air density, lbs-ft~3
A = main or branch loss coefficient,
dimensionless
2.4 Negative Loss Coefficients
By investigating figures 2 and 5 it may be noted that one or the other coefficient
may be negative. This can be best illustrated by the following example and sketch.
For an area ratio of 19.3 from the main to the branch, and a velocity ratio of 0,89
from upstream of the main (U) to downstream
-0,075; while the tee-branch coefficient is
of 2.15, In effect, the branch Jet at
is moving at ft/min, has an asperating
ration phenomenon, also noted by Healy (7),
are connected to relatively large mains.
(D) the tee-through loss coefficient is
+3.55 for a velocity ratio from (B) to (D)
ft/min coming into the mainstream, which
affect or acts like an ejector. This aspl-
becomes predominant as smaller branch ducts
This illustration actually occurred in one of our industrial power plants where
the noise generated due to the high velocities is not a problem. These relatively high
velocities are a result of our system design philosophy, which decreases the size of
the branch until the total pressure for the main and branch duct systems are approxi-
mately the same. For systems in which noise would be a problem the branch diameter
would not be decreased, but rather, resistance added in the branch by other means such
as obstructions. In most applications high velocities would not be encountered, and
both the main and branch coefficients most likely would be positive.
378
3. References
(1) F. Petermann, "Der Verlust In Schlef-
wlnkllgen Rohrverzwelgungen" , MHITHM
(Mlttellungen des Hydraullschen
Instltuts der Technlschen Hochschule
MUnchen), Heft 3, , PP. 98-117.
(2) U. Inoue, "Duct Design Handbook",
Waseda University, Japan,
(3) G. Vogel, "Untersuchungen liber den
Verlust in rechtwinkligen Rohrver-
zweigungen", MHITHM, Heft 1, ,
pp. 75-90.
(4) G. Vogel, "Untersuchungen ifber den
Verlust in rechtwinkligen Rohrver-
zweigungen", MHITHM, Heft 2, ,
pp. 61-64.
(5) C. M. Ashley, et al, "Branch Fitting
Performance at High Velocity", ASHAE
Transactions, Vol. 62, , pp. 279-
294.
(6) W. K. Brown, Jr., et al, "Friction
Loss Characteristics of Branch Duct
Fittings with a Fixed Duct Configura-
tion", ASHRAE Transactions, Vol. 72,
Part I, , p. 346.
(7) J. H. Healy, et al, "Pressure Losses
Through Fittings Used in Return Air
Systems", ASHRAE Transactions, Vol. 68,
, pp. 281-295.
4. Acknowledgement
We are grateful to Mr. Y. S. Chen of the University of Kansas for indicating the
availability of Petermann 's data as summarized by Dr. Inoue and the discussions with
respect to the significance of the negative loss coefficients.
379
o
sseiuoTSueuifp '{HJ,a3iL Jo Wy) ^jusf of jjaoQ ssoi q3noj:qj,-88j,
380
381
C TOTAL PRESSURE LOSS COEFFICIENTS IN THE THROUGH SECTION OF A RETURN AIR
C 45-DEGREE TEE (TEETH), DIMENSIONLESS
C
C ARDB IS THE AREA RATIO OF THE TEE MAIN TO THE TEE BRANCH, DIMENSIONLESS
G
C VT^UD IS THE VELOCITY RATIO PROM UPSTREAM OF THE TEE MAIN TO DOWNSTREAM OF THE
C TEE MAIN, DIMENSIONLESS
FUNCTION TEETH ( ARDB, VRUD)
HPRIM=0 . /ARDB**0 .
H=1.0-HPRIM
T=H-VRUD
YK=0. -0. 59^6*H
C=-l . 46l*ARDB**0 .
C0EF=C*T**2
TEETH=COEF+YK
RETURN
END
Figure 3. Fortran Function Subprogram Listing for
Detennlning Tee-Through Loss Coefficients
Velocity Ratio, Branch to Downstream (VRBD), dlmensionless
Figure 4. Comparison of Brown's and Petermann's Branch Coefficients
382
C TOTAL PRESSURE LOSS IN THE BRANCH OF A RETURN AIR 45-DEGREE TEE (TEEBR),
C DIMENSIONLESS
C
C ARDB IS THE AREA RATIO OF THE TEE MAIN TO THE TEE BRANCH, DIMENSIONLESS
C
C VRBD IS THE VELOCITY RATIO FROM THE BRANCH TO DOWNSTREAM OF THE TEE MAIN,
C DIMENSIONLESS
FUNCTION TEEBR (ARDB, VRBD)
A=1.
B=0.
R= ( A/ARDB**0 . 5 ) - ( B*VRBD/ARDB**0 . 5 ) + ( VRBD»*2 )
TEEBR=R-1.
RETURN
END
Figure 6. Fortran Function Subprogram Listing for
Detennlnlng Tee-Branch Loss Coefficients
384
Automatic Design
of Optimal Duct Systems
M. Kovarik
Commonwealth Scientific and Industrial Research Organization
Melbourne, Victoria, Australia
A system of ducts for the delivery of air in an air-conditioning installation
subject to pressure-balance conditions is found to be indeterminate and thus
capable of satisfying additional conditions. Upper bounds are imposed on the
air velocities in some sections and the problem of economically optimal
diameters is formulated as a constrained non-linear programming problem.
This is transformed into an unconstrained problem capable of solution by
known numerical methods. A computer program based on the concept of
Lagrange multipliers and the Newton-Raphson iterative method is outlined.
Techniques for acceleration of convergence are stated. Properties of resulting
optimal solutions are discussed.
Key Words: Ducted flow, friction losses, annual cost, capital cost,
running cost, kinetic energy, potential energy, static regain.
1. Scope and Definitions
The duct system under discussion consists of several sections, each of a uniform equivalent
diameter along its entire length. If a section contains bends, it will be represented by a straight
section of an equivalent length, according to conversion formulas summarised by Carrier and
others [ 1] ^ . Each section terminates either in a divided flow fitting or in a terminal outlet. Each
divided flow fitting has one inlet and two or more outlets. One of these outlets may be a terminal
outlet, others connect to the inlets of further downstream sections. There is only one entrance
section. From the description, it follows that there are at least as many sections as terminal outlets.
A run is a set of duct sections commencing at a terminal outlet and continuing upstream to the
inlet of the entrance section. The number of runs is equal to the number of terminal outlets.
2. Balancing Conditions
To maintain the required flow of air at each terminal outlet, it is necessary that the sum of
pressure drops along a run, plus the pressure at its outlet p is equal to the inlet pressure p^ for
all runs:
Pi = ^^Pjk + ^^Pl + Po
The summations extend over all sections 1 of a run and over all divided flow fittings connecting
section j to section k along the same run. The singly subscripted pressure drops result from friction
losses, doubly subscripted ones from the application of Bernoulli equation at the divided flow
fittings, as shown in Appendix 1. For given section lengths, flow quantities and fixed shapes of
divided flow fittings, the pressure drops Ap of eq (1) are functions of equivalent diameters of the
corresponding sections.
For a system with M + 1 terminal outlets, there are M + 1 equations of type (1), one for each
run. By subtracting the first of these from each of the remaining ones, the inlet pressure is
eliminated and M equations are obtained in the following form:
Figures in brackets indicate the literature references at the end of this paper.
385
^APjk + ^^Pl - ( ^^Pxnn ' l^P,) - 0 (2)
These M simultaneous equations will be written as
H(D) = 0 (2a)
where H is an M x 1 matrix of the left hand side of eqs (2) and the argument D is an N x 1 matrix of
the equivalent diameters of all the N sections. As the number of sections is at least equal to M + 1
and each section may have a different equivalent diameter, there are N independent variables
available to satisfy M < N simultaneous equations. Thus the balancing equations have no unique
solution. Consequently, a duct system corresponding to the description of Section 1 is always free
to satisfy at least one condition in addition to the balancing conditions.
3. The Degree of Freedom
The difference between the number of sections N and the number of balancing equations M will
be called the degree of freedom of a duct system. In systems of one degree of freedom, only one
section diameter or velocity may be freely chosen, all others are determined by the balancing
equations. Where the degree of freedom exceeds one, the design problem is complicated and while
different feasible designs may be evaluated by comparison, it is difficult to estimate how much better
the best possible design might be. In the following, the problem of optimal duct system will be
posed, analysed, and a computer program for the determination of optimal dimensions will be
described.
4. Criterion of Optimality
A duct system which delivers required quantities of air at the required outlet pressures may
suffer from only two major shortcomings: excessive costs and noise. Standard reference literature
[3] suggests empirical rules for maximum permissible air velocity in various duct sections. The
computer program to be described provides means of incorporating arbitrary upper bounds on any
air velocity in the system.
Having satisfied requirements relating to noise, a duct system may be optimised with relation
to costs. For given layout, section lengths, air quantities, duty period, types of divided flow fittings
and unit cost factors, the total cost of the system depends on the transversal dimensions. It will be
analysed on the basis of equivalent diameters.
5. Costs
All capital costs will be reduced to their annual equivalents, following standard accounting
practice [2]. The annual capital cost of section j of length Xj and diameter Dj is
C. = q.X..(a + a,S,D. + a.,S,D^ ) (3)
j^j^ollj22j' ^ '
where q is the capital recovery factor and the a's are unit cost factors. The first of these, a.Q,
reflects costs dependent on the length alone, aj^ represents the component of cost related to the duct
surface area, a^^ stands for the rental value of the space occupied by the duct section. Any two of
these three factors may be simultaneously zero. The factors S]^, S2 relate the equivalent diameter
to circumference and to the cross-section area; in a circular duct, they are 11 and n/4 res-
pectively. For rectangular ducts, analogous factors follow from Ref. [4].
The annual capital cost of the duct system is the sum
C(D) = I C. (4)
over all the sections. According to eq (3) it is a quadratic scalar function of the equivalent diameter
matrix D.
386
The running cost of a duct system is the cost of energy necessary to maintain the airflow for
the required time. The power applied at the entrance section is
P = Ql ■ Pi(D) (5)
where Pj^ is the total pressure at the entrance of the system and Q^^ is the air flow rate. The
derivation of p;^ is in Appendix 1. For an overall motor-fan-diffuser efficiency e, the running cost is
r^D) = e"^ a3 t P(D) (6)
where a^ is the cost per unit of energy at the motor and t the total time of running per year.
The total annual cost is then
C^(D) = C(D) + r(D) (7)
As the pressure increments which combine to determine the running cost are proportional to
velocity to a power of approximately 2 (see Appendix), r(D) is a function of diameter raised to a
power of approximately -4. The capital cost is a quadratic function of diameter and both C(D) and
r(D) are, of course, positive. Thus C.-p(D) of eq (7) is a convex function and satisfies second order
necessary conditions in the sense of Ref. [5] for the local uniqueness of the optimal solution.
6. The Constrained Problem
The problem of optimal duct system design may now be formulated:
minimise Crp(D) (8a)
subject to H(D) = 0 (8b)
and D. - B. > 0 (8c)
1 1 — ^ '
where Bj^ is the lower bound of diameter corresponding to the prescribed upper bound on velocity
in section i.
This is a non-linear programming problem with accessory conditions (8b) and unequality
constraints (Be). Techniques of solution are summarised by Fiacco and McCormick [5] , who refer
to this form as Problem A. A particular technique embodied in a working computer program for
iterative solution of optimal duct diameters will be described.
7. The Unconstrained Problem
The constraints (8c) are represented by ficticious costs; if, during the computation, any
diameter Dj^ becomes smaller than the corresponding constraint Bj^, the cost of section i is
increased by a quantity proportional to the square of the excess Bj^ - D^. This increase is applied
with sufficient weight, so that the resulting optimal diameter is within a prescribed tolerance
interval of the applicable bound. Thus, the constrained problem is transferred into an unconstrained
problem with accessory conditions:
minimise C-p(D) (9a)
subject to ^j(-^) ^ °' 1 1 j £ (9b)
where C-p is the sum of actual and ficticious costs:
Cj, = Cj, + I k. (B. - D.)^ (9c)
387
being the ficticious cost factor
k. = 0 if B. < D. (9d)
k. > 0 if B. > D. (9e)
j
The solution of problena (9) is a set of N diameters Dj^ constituting an N x 1 matrix D which
satisfies eq (9b) and the condition for extreme value
aw
aD,
(10)
for all i's. Here, W is the Lagrangian
W = + u'^H (11)
consisting of the cost and the M balance condition Hj (D) = -0;- is the M x 1 matrix of Lagrange
multipliers, transposed. (For a brief outline of the Lagrangian technique, see reference [6])
The design problem now consists of finding the N values of and M values of Uj which
simultaneously satisfy eqs (10) and (9b); these are M + N independent conditions binding an equal
number of variables.
The numerical solution commences by choosing a tentative initial set of values for the Lagrange
multipliers Uj, solving eq (10) for the corresponding diameters Di(U) and substituting these into
eq (9b). Due to an error in U, the left hand side of eq (9b) is not equal to zero, but to an error
matrix E dependent on U:
H(D(U)) = E(U) (12)
A better set of multipliers is obtained from the initial one by Newton-Raphson method [7]. A
correction 5U in the values of U which reduces the error E is calculated from the first order
approximation:
E + -fg. 6U = 0 (13)
This equation is solved by inversion of the M x M matrix SH/ aU:
5U = -i-ff . E ■ (14)
The original values of U are corrected by 6U and the procedure is iterated until the residual
error E is reduced within prescribed bounds. The physical significance of E is the amount of
pressure unbalance in the duct system.
The matrix BHI dU is obtained as the derivative of a composite function:
au ao dU ^ '
All elements of the M x N matrix dlil dD are available in analytical form following substitution
into eq (2a) from eq (2) and from the pressure drop expressions in Appendix 1 . The N x M matrix
ao/ au is obtained from the Lagrangian eq (10) by the rules for derivatives of an implicit function.
The typical element is
388
dD.
i_
dU.
az.
1^
au.
J_
az.
i_
ao.
1
(16)
where = , from eq (10).
i
The denominator dZ^I dD^ in eq (16) is the second partial derivative of the Lagrangian W in
respect of D^^.
8. Convergence
The iterative process converges slowly and it is necessary to use special precautions to
ensure stability while the initially chosen values of U are far from the correct ones. The program
limits the step size and restricts, in the initial stages, all diameters by cost penalties based on a
rough estimate of optimal diameters. These penalties are cancelled when stability is reached and
have no effect on the result.
9. Properties of Optimal Duct Systems
The duct system resulting from the above procedure differs to some extent from systems
designed by current methods. The difference is minimal in systems of one degree of freedom,
i. e. those where the number of sections is equal to the number of terminal outlets. The static
regain method [8] uses physical concepts employed in the setting up of balancing conditions, eq (2a)
and eq (2c), Appendix 1 of the present study. With one degree of freedom, the system is determined
by any single variable being fixed; it follows that any such system is optimal for some set of design
parameters. However, these may equal the parameters actually applicable only by coincidence.
TABLE 1
SYSTEM OF ONE DEGREE OF FREEDOM
DESIGN A:aj = 1 . 50 $/ft^ DESIGN Btaj = 16. 70 $/ft^
DUCT
SECTION
LENGTH
ft
Q, CFM
DIAM.
INCH
VELOCITY
ft / min
DIAM.
INCH
VELOCITY
1
50
10, 000
38. 1
1,261
24. 0
3,185
2
40
8, 000
36. 3
1,115
23.4
2, 680
3
20
6, 000
32. 6
1 , 036
21.4
2, 412
4
20
4, 000
27. 8
949
18. 6
2, 127
5
20
2, 000
20. 9
837
14. 3
1 , 795
CAPITAL COST, at a^ = 1 . 50 $/ft
ANNUAL CAPITAL COST
RUNNING COST at hrs/year
0. 02 $/kWh
TOTAL ANNUAL COST
$1 , 957
$184. 74
$42. 11
$226. 85
$1 , 263
$119. 30
$294. 50
$413. 80
System of one degree of freedom, for Table 1
389
Table 1 compares two optimal systems of one degree of freedom, differing only in the capital
cost factor aj , the cost per unit area of the duct surface. Both systems have been obtained as results
of the procedures described above. Design A is optimal for a realistic value of aj = 1. 50 $/ft^;
design B would cost 82% more to own and operate in the same cost environment. It happens to be
optimal for duct cost 16. 70 $ I it^ . Design B consists of sections 10 - 14 of an example given in
Ref. [9]. The example quoted may, of course, be optimal for a lower capital cost and a shorter
duty period.
For systems of degree of freedom higher than one, the current design methods offer no unique
solution. Thus, there is no basis for economic comparisons between them and the present method.
It is true, however, that while static regain systems of degree one are inevitably optimal, even if
perhaps for some unrealistic cost factors, higher degree systems may only be optimal by an unlikely
multiple coincidence.
To understand the shortcoming of existing methods, it is necessary to realise that a duct system
supplies two things to each divided flow fitting: the air to be distributed and the energy to drive it
through the subsequent sections. This energy exists in two forms: kinetic and potential (static
pressure). The static regain method, consisting in a "procedure in which the duct is sized so that
the increase of static pressure or regain at each take off offsets the pressure loss of the succeeding
section of the run" [10] transports all this energy as kinetic. This involves friction losses upstream
whereas transport in the form of potential, or pressure, is free from losses in systems without leaks.
On the other hand larger ducts are required to reduce the kinetic energy content. The present
procedure optimises the proportion of kinetic to potential energy according to the criterion of
minimal costs, subject to balancing conditions and velocity constraints.
10. Re
[1] Carrier, W. H. , Cherne, R. E. , Grant, W.A. ,
Roberts, W. H. Modern Air Conditioning,
Heating, and Ventilation, Third Edition,
pp. 256-7, (Pitman, )
[2] Ibid. p. 513.
[3] ASHRAE Guide and Data Book, Systems and
Equipment for , p. 37 (American Soc.
of Heating, Refrigeration and Air-Condit-
ioning Engineers)
[4] Ibid. p. 29, eqs (6).
[5] Fiacco, A. V. and McCormick, G. P. Non-
linear Programming: Sequential Uncon-
strained Minimisation Techniques
(Wiley )
:ferences
[6] Korn, G. A. and Korn, T. M. Mathematical
handbook for Scientists and Engineers
(McGraw-Hill )
[7] Ibid, section 20. 2-8.
[8] Ref. 1 , p. 261.
[9] Ref. 3 , pp. 42 - 44, Table 9,
sections 10 - 14.
[10] Ibid. p. 39, Col. 2.
390
APPENDIX 1
Pressure Drop Formulas
The following expressions are based on the ASHRAE Guide [3]. Equation (1) is the SI equiva-
lent of formula Z5, p. 39. Equation (2) is a generalised form corresponding to formulas 14, 16-20
of page 35. Any of the guide expressions may be obtained from eq (2) by a suitable choice of
parameters Cy, Cq.
The remaining equations of this Appendix are derived from eqs (1) and (2).
Symbols and Units
p
air density
(kg m'-^)
(m s )
V
air velocity
Di
equivalent diameter of section i
(m)
Li
equivalent length of section i
(m)
/ 3 -1>
(m s )
Qi
flow rate in section i
Api
pressure drop in section i
(N m"^)
^Pkl
pressure drop due to a divided flow
fitting connecting section k to
section 1
(N m'^)
In a duct of circular c ros s - section the pressure drop resulting from friction is
Ap. - 0. . L. . Q^-^^ . D"^-^^
1 111
(1)
The pressure drop corresponding to a transition from section j to section k would be, in a
loss free system
f (^k
(2a)
Introducing coefficients C-y and Cj-j to represent losses occurring upstream and downstream of the
divided flow fitting, we have
_E_
2
^D ^k
C., v^
U J
Expressing the velocities by flow rates and diameters
V. = S-,
Q. D'^
1 1
(2b)
(2c)
where 82 is the proportionality factor between D and c ros s - section area for the particular shape
employed
The total pressure at the entrance of the system consists of the velocity head and of all the
pressure drops along any run.
2
'1 + I Ap. + I Ap.j^ + p
(2d)
(3)
and the necessary fan power is
Qj . P
(4)
which leads to eq (5) of Section 5.
The first and second partial derivatives of the running cost in respect of any diameter follow
after substitution into eq (3) for Vj and all the pressure drops from eqs (1), (2a) and (2d).
391
A System of Computer Programs
Widely Used in Europe for Designing,
Selecting and Analysing Different
Air Conditioning Systems
1
A.VJ, Bo eke and S. Larm
Delft University of Technology, Netherlands
and
AB Svenska Flaktf abriken , Stockholm, Sweden
The ultimate object of using computer programs in air conditioning design is
to make feasible an optimal choice and integration of building features and A.C.-
equipment that complies with indoor environment requirements. To this end it is
necessary not only to compute heating and cooling loads in all individual rooms
for specified room temperatures and outdoor conditions, but also to obtain the
data required for directly selecting all main central eurid peripherial components
of the A. C, -plant from maniif acturers ' catalogues and to assess the average yearly
energy consumption. These items are substantially influenced by the type of
plant chosen and the interaction of the different loads handled simultaneously in
all zones. Further, heat storage capacities cooperating with tolerated uncon-
trolled variations of room temperatures within specified limits, moving shadows
from other buildings, control systems and setting values, causing annihilation
and/or recuperation of energy etc., play an essential part. In this paper a set
of computer programs is presented which yield all the information mentioned for
different kinds of A. C. -systems in addition to many other valuable data, such as
temperature curves occurring in rooms without air conditioning. There is also a
prograjn for the calculation of complete duct systems. Manuals and take-off-
sheets are available in different languages and units systems. Computer results
are printed in corresponding varieties. The programs are used in many countries
in Europe and several hundreds of projects have hitherto been calculated. As a
result of these programs there is now a growing practice for architects, together
with civil, electrical, acoustical and A. C. -engineers, etc., to form a team as
early as the financial stage of the planning, thus obtaining an optimal total
design without individual dominance of any part concerned.
Key Words: Air conditioning, A.C. central systems,
A.C. load calculations, A.C, plant design,
computer calculations.
1. Introduction
In articles and discussions about the application of computers in A.C. -design work one often
meets the opinion that this application would be identical with and confined to the computerized
calculation of maximum heating and cooling loads per room - and possibly the dimensioning of duct
systems.
Without denying the importance and extensiveness of these basic calculations, every A.C.-
designer knows very well that they constitute only a minor part of the entire work. They do not
give him any ajiswers to questions such as total cooling and heating energy consumption in the entire
building - consisting of many different rooms - during a normal year, determination of size of room
units and central plant in such a way that room temperatures are allowed to glide freely within certain
specified limits, setting values of different control functions, etc.
These, and many similar items, are dependent on the way in which the calculated net heating and
cooling demands are satisfied, and on the thermo-dynamic losses and regain possibilities inherent to
the A.C. -system chosen. A complete package of application programs within the A.C. -field should there-
fore incorporate not only the necessary load computing routines, but also the digital simulation of
most current A.C. -systems.
Professor and Engineer, respectively
393
For this reason, in I964 we started to develop such a set of programs (see fig. I), the second
generation of which have already been in extensive daily use throughout Europe for several years and a
third generation are now being completed and are already partly operative.
2. Survey of Computer Programs Developed
When planning a new building in moderate European climate areas the first qriestion posed by archi-
tects and principals is often whether an A. C. -installation is in fact necessary, or whether an acceptable
indoor climate could be maintained by a simple ventilation system. The prime decisive factor in this
case is the air temperature attained in the rooms during the hottest part of the year. Therefore a
special prograjn has been established which calculates the course of daily room temperature variations
without air-conditioning, and without or with mechanical ventilation at a given rate and temperature.
Of course all given structural characteristics and specified conditions as regards the use of the
building and the local outdoor climate are taken into consideration in this calculation.
If the need for aji A. C. -installation is found to exist, the necessary equipment can be determined
and the operating costs be evaluated by using the other available programs for the calculation of,
respectively:
A. Net heat gains and losses per building module for all relevant average ajid design
conditions such as normal workdays and holidays during clear aind cloudy weather
throughout the year (Program LK012).
B. Installation and operating data for:
Two-pipe induction systems with variable primary air temperature (Prograjn LK022).
Four-pipe induction systems (Program LKO42). This program can also be used for
calculating two-pipe terminal reheat systems.
Ihial-duct systems (Program LK062).
C. Dimensions of duct systems made up of sheet metal ducts of circular sections and
consequent fan pressures (Program LK002).
3. Particulars of the Programs
3.1 General Observations
When the work of calculating is entrusted to a computer it becomes feasible to take full consider-
ation of such factors as non-simultaneousness of maximum cooling demands, heat storage in the building
structure in connection with irregular times of insolation due to moving shadows, etc.
The potential of the computer has not been fully utilized if it is merely employed to carry out the
same table references and calculations as the designer has previously performed manually. On the other
hand, the program designer should not seek theoretical perfection. This could easily result in the loss
of other important attributes, such as wider usefulness, since there is a limit even to the capacity of
computers.
An excessively thorough treatment of certain factors in the calculation process may also frequently
result in the take-off sheets being so extensive in scope as to daunt the ordinary, practical design
engineer.
Moreover an unlimited refinement of the calculation methods entails a rapid increase of the CPU-time
in the computer and so a sensible balance between calculation costs and scientific perfection must always
be observed.
3.2 Meteorological Data
This philosophy is also apparent in the method we have adopted for the specification and subsequent
use of the meteorological data. The calculation requires a continuous course of outdoor temperatures
during an average and a design-day in every month under clear and overcast weather conditions. These
temperatures are calculated by the computer on the assumption that the daily variation describes a sine
curve (vjith alternate long and short half-periods), the maximum and minimum points of which are given in
a special meteorological data form.
When a calculation is to be carried out for a specific geographic area for the first time, the
requisite climatic particulars must be entered on this form. The particulars are then filed for
future reference.
394
The varying hvunidity of the outdoor air is treated in a similar majoner. For direct ajid diffuse
solar radiation intensity only information as to the maximum values for a clear day in each month is
required. The variation in intensity during the day is then calculated by the computer for every
required aspect by assuming that direct solar heat striking an external wall varies during the day from
zero to a maximum value and back to zero in conformity with the positive portion of a sine curve. The
half-period is equal to the time between the instant when solar radiation first strikes the facade and
that at which it ceases to strike it, regardless of whether these points in time are determined by sunrise
and/or sunset, or by the sun appearing and/or disappearing round the cprners of the facade.
3.3 Basic Calculation Method
The variation of room air and wall temperatures and of heating and cooling demaJids per module is
calculated by determining the balance of heat stored in the building mass and trajnsferred to the room air.
This balance is computed hour by hour and includes all internal and external heat gams and losses. The
heat balance at a certain point of time, called "the hour (CL+T)" is calculated with the assumption that
outdoor conditions, solar radiation, as well as internal heat loads that do not vary with room temper-
ature are constant from the preceding point of time, "the hour CL" for which they were given or pre-
viously calculated, until and not including the hour CL+T. If the room air temperature varies it is
supposed to be subject to a sudden change immediately after the hour CL and then to remain constant until
and including the hour CL+T. Those heat loads which depend on room air temperature (e.g. transmission)
as well as the wall surface temperature and the wall core temperature are supposed to vary in the Scune
manner.
The results of each heat balance calculation are new values of wall surface and wall core temper-
atures for the hour CL+T as well as a new room air temperature to be reached at that hour or, when room
temperature is prescribed, a new cooling or heating demand. Thus a "backward discretization of time"
is applied avoiding any instability in the calculations.
Calculations are started from 1 a.m. on the assumption that both the air in the room and the walls
and floor have a temperature of 71°F then. After calculations have been completed for a full 24 hours,
the room and wall temperatures obtained are usually different and these new values are taken as starting
points for the next day, and so forth. Calculations are carried out in this way for four consecutive
days, in general, this being adequate in most cases to achieve a stabilized temperature history i.e. , the
values for 12 p.m. are largely identical with those calculated for 1 a.m. the preceding night. In
buildings with heavy structures, however, stabilization may not be achieved at the end of the fourth day
calculated and therefore the number of consecutive days can be changed arbitrarily. In most cases,
though, this number is limited to four days in view of the fact that the majority of 'heat-wave' periods
(representing design weather) seldom last longer than four days, at any rate in Western Europe type
climates.
3.4 The Influence of Sudden Load Variations,
Manipulation of Blinds, etc
Using the method described, it is also possible to take account of sudden load changes, such as the
switching-on or off of the lighting, the drawing or rolling-up of sunblinds, or the start and finish of
office hours with the associated change in the required room temperature, occupant load, heat gain from
lighting, etc. The cooling requirement in an office, for example, is greatly affected by assumptions
such as that Venetian blinds will be drawn all day on sunny days, or that they will be drawn only when
the sun shines directly on the wall concerned during office hourse.
The take-off sheets provide for an indication of the times between which office hours may be assumed
to lie, and the temperature limits to be maintained during these hours eind at night or during holidays.
As stated previously, the solar heat gain through the windows is calculated for each hour. The program
maJces the assumption that when this gain exceeds a certain level the sunblinds will be drawn, as long as
the room is occupied. Otherwise it is assumed that the blinds, etc., are not drawn. Outside office
hoxirs, the client may specify that blinds will always be drawn or open.
Similarly, the light intensity due to natural lighting at a given distance from the windows is cal-
culated for each hour of the day. It is assumed in the program that when this falls below a certain
level the artificial lighting will be switched on and the heat gain from this source is then included in
the heat balance equation for the hour concerned. It is taken for granted in this context that lighting
is likely to be switched on only during office hours. When the intensity of natural lighting in the
room is on the increase, so that it exceeds the limiting value up to which supplementary lighting is
required, then it is normally assumed that artificial lighting will be switched off. It is possible,
however, to provide for a degree of 'lighting negligence' by assuming that once the lighting has been
switched on it will be left on to the end of office hours, regardless of the subsequent need or other-
wise.
395
' 3.5 Effect of Shadows from External Wall Projections
and Other Buildings
The reduction in the solar radiation through windows depending on shadowing by external wall
features such as balconies or columns, or to the recessing of windows is taken into due account. This
reduction will naturally vary according to the angle of incidence of the sim's rays, i.e. according to
the time of day, and is calculated stereometrically on the basis of the sun's varying altitude and
azimuth at the geographic latitude concerned.
The tables published in current A. C. -design manuals which are normally used to determine 'storage
factors' are limited, for practical reasons, to external walls on which there are no shadowing features.
This meauis that in such manual calculations the same reduction factor for shadows is employed not only
for the direct solar radiation at the time considered, but also for the solar heat stored during the
preceding hours. This may lead to tangible errors in certain cases, but these are completely eliminated
in the computer programs, which calculate the shadow factor and stored heat hour by hour.
The programs also permit moving shadows from other neighbouring buildings or parts of the same
building to be taken into account. The edge of such shadows moves constantly and, at any given time,
the different parts of the facade will have been in sunlight for different lengths of time. The stored
solar heat will therefore be different for these different parts and thus the resultant room temperatures,
or the cooling demand will differ also.
A maximum of 12 shadowing rectangular buildings can be allowed for. Buildings with complex shapes,
such as horizontally or vertically L-shaped structures, are considered to consist of two or more adjacent
single rectangular buildings. The locations of the corners of the shadow-throwing structures in re-
lation to the facade investigated are defined by means o:" a co-ordinate system which can be laid
arbitrarily over a site plan of the building area (see fig. 2).
A division of the facade into a maximum number of 100 surface elements is then assumed by the computer.
The sequence of room air temperatures or thermal loads is calculated for one module in every such surface
element or group of elements. The different local successions of sunny and shaded periods on every part of
the facade are thereby taken into account and also the corresponding switching on and off of electric
lighting, the drawing and opening of sun blinds and the storage effect due to these factors.
4. Lay-out and Versatility of Take-off Sheets
For every program only two different kinds of take-off sheets are used. One of these contains all
the data which are common for the entire building or describe the basic conception and central control of
the A. C. -plant, whereas the other contains all the data pertaining to each individual "zone" or group of
identical modules.
In addition to comprehensive instructions given in the "Program Users Manuals", the take-off sheets
contain a considerable amount of guiding text to facilitate the filling-in. This is illustrated in
figure 3 showing the "Common Plant Data"form for the four-pipe induction system program (LKO42).
Within each A. C— system many alternative variations can be specified such as different combinations
and consecutive orders of components in the central air treating unit, free cooling through "dry" or
"sprayed" recovery coil, automatic or manual terminal unit control, etc. J:\Lrther, the user can specify
by how many deg. F personnel in a room should be able to regulate the room temperature upwards or down-
wards, by how many degrees the room temperature should be allowed to glide upwards above the normally
desired value in the event of exceptionally hot weather (at summer design temperature), whether 'lighting
negligence' is to be taken into consideration, ajid so forth.
5. Calculation Results
5.1 PLOom Temperature Program
The results of the room temperature program LKOI5 comprise one printed page for every building zone
and month investigated. Vlhen moving shadows occur on a facade this page gives the daily range of room
temperatures obtained in the two facade elements in which the highest and the lowest top values, respect-
ively, of the entire facade occur on a clear day. Further, the print-out gives the temperature range
obtained on a cloudy day during which all modules, of course, are subject to equal loads.
VJhen the computer, on the basis of prevailing solar intensity at any point of time, states that
lighting should be switched on or that Venetian blinds, jalousies or similar devices should be shut, this
is indicated by the letters 'L' and 'J' respectively, after the room temperature value at the hour in
question. In addition frequency tables are printed giving information on the percentage of the total
time of occupancy in the zone during which different room temperatures are reached or exceeded. The
varying boimdary line of the moving shadows is also shown in the computer results, (fig. 4)'
396
5.2 Basic Load Calculating Program
The results obtained with th^ program LK012 include the heating and cooling requirements per module
during any specified month or all 12 months of a statistically normal year, as well as the maximum re-
quirements occurring under outdoor design conditions. These results are based on room temperatures
being prescribed either at fixed values or between given limits.
The normal procedure following this calculation is to use the data calculated and stored by the
computer for designing aji A. C. -installation with the aid of one of the "plajit programs". However, in
many cases the result of the LK012 program has a value of its own - for instance when different
alternative building featiires such as size of windows, kind of blends, etc., are to be compared.
5.3 Plant Designing Programs
An example of one page of the results produced by the plaJit designing programs {LK022-LK062) is
shown in figure 5. This page supplies, for one zone, the information necessary for the selection of
the induction units in a four-pipe system (max. required unit coil cooling and heating capacities in
connection with primary air supply). Comments are also printed as to the specified comfort require-
ment or some other consideration that has been decisive for the capacity values stated.
In addition, a number of tables are printed showing the varying thermal output of the induction unit
during the day together with room temperatures actually obtained for several critical running conditions .
In the results of the dual-duct plant program (LK062) corresponding information is given concerning
the chao'act eristics of the mixing boxes.
When moving shadows occur on any facade a special table is printed indicating on which parts of
that facade it is possible to install terminal units with a lower capacity than the maximum required
capacity owing to the reduced solar heat gain in these parts. After determining the capacity of the
induction units or the mixing boxes, the computer calculates the total heating and cooling energy con-
sumption in the whole building for all consecutive hours of a clear, as well as a cloudy day in every
month. This is done both for normal and extreme ("design") outdoor conditions.
The highest value of the total momentary cooling demand (including all required sensible and latent
cooling of outdoor air) which the computer encounters in the course of this calculation is stored and
later shown in the printed calculation result. The result, apart from the maximum total cooling load,
also states the daily course of unit outputs and room temperatures in every zone during the day on which
this maximum total load occurs (fig. 6).
In addition to the design cooling load with the appropriate times and temperatures, the maximum
total heating demaJid and a large number of other data required for the design of the plant, such as
central cooling ajnd heating coil characteristics, total water flow rates, etc., are also provided.
The total consumption of heating and cooling energy at every hour, calculated over the normal year
referrred to above, is collected in a number of items so that the totals may be obtained at the end of
each month and of the whole year. These totals are composed of the summed-up hourly consumption
figures obtained in "real" (digitally simulated) over-all plant operation during clear and cloudy work-
days and weekends in statistically correct proportions for every month. Apart from the yearly totals,
the over-all energy consumption is stated per hour and per month.
5.4 Duct Calculating Program
After determining all main thermal components in the way described above, the dimensioning of the
duct system and the fans remains to be calculated. This is done with the aid of the duct system cal-
culating progrcun (LK002).
This program yields all the necessary information for each individual pipe section of the system
such as quantity of air passing, air velocity, pressure loss and, in the case where the pipe section
ends in a supply or extract point, the available static pressure at these points. Any throttling
devices required are indicated on the appropriate sections giving the pressure drop need. The diameters
of the pipe sections and the throttling devices that may be required at the main junctions are given
final values by the computer, often after repeated calculations in order that a certain maximum permis-
sible pressure difference between the different supply points will not be exceeded. The table f\irther
indicates the total quajitity of air and the faji pressure.
Fiirther, the results of this program include a complete list of the total lengths of all ducts of
different diameters used in the system, as well as the total number of bends, tees, etc.
397
When recfuired, the print-out can also include a sub-division of the list in accordeunce with the
different stages of erection of the building. Each partial list then comprises the ducts and acces-
sories required for one floor, wing or similar part of the building and the erection engineer is thus
provided with means to order the duct parts for delivery to the building site in smaller portions just
when they are required.
6. Practical Applications and Consequences
Amongst air-conditioning engineers in Europe there is a general wish to be involved in the planning
of new buildings at as early a stage as possible in order that the architectural design and the lay-out
of the A. C. -plant should be co-ordinated from the very beginning, and this desirability is pointed out
on every possible occasion.
However, this recommended teamwork has only too seldom been applied in actual practice. One of
the main causes of this regrettable state of affairs has most probably been the difficulty for A.C.-
people to give immediate and correct answers to essential questions raised by architects and principals.
Such questions are, e.g., "How does the glazing percentage of facades influence costs and required space
for cooling equipment?" or "What type of A. C. -system is the most advantageous m ajiy given case?"
During the last couple of years, however, a noticeable chaJige in this situation has taken place -
made possible by the development of computer programs such as those described in this paper.
An increasing understanding by architects and building owners of the importance of air-conditioning
and of the problems involved can be observed. Thus, there is now a growing practice for all the parties
concerned in the planning of a building to form a team already at the financial stage, resulting in an
optimal total design.
398
ROOM TEMPERATURE
CALCULATING PROGRAM
LK015
2-PIPE INDUCTION
SYSTEM WITH VARYING
AIR TEMPERATURE
LK022
BASIC LOAD
CALCULATING PROGRAM
LK012
^-PIPE INDUCTION
SYSTEM
LK0/;2
DUAL DUCT SYSTEM
LK062
DUCT CALCULATING
PROGRAM
LK002
Pig. 1 Basic conception of a set of A. C. -design programs
399
Fig. 2 Configuration of buildings with site plan
400
SVENSKA
•l.AK 1 F VBRIKEN
EDP-calculation for air conditioning pJontu
Foiir pipe iniiijction ayBtem.
Ponii BK DEE
ProKroin LKO/12
CUMMON PLANT DATA
Cardn^ber I fl L |K| 0 | 4 | 2 | [3]
N^e or oo. Oi- Wildine iVl l^l I I I 1^ I I I I I I I TTTT" I I I I!
Reference- and job number (filled in by SP) .
Mark with 1 if!
Calculation of required capacities
and central control only (Part l)..
•0
Calculation of energy consumption and
cooling plant only (Part 2). It is aesumed i — i
that calculation of Part 1 has been made earlier L_J
COOLING PLANT AND REQUIRED COIL CAPACITIES
Mark with 1 if:
Cooling plant to be determined with r~~]
regard to light load a clear day«"l I a cl
When dimensioning cooling plant and required coil
capacities continuous running is assumed
Heating demand at design winte
period of holidays
calculated for a workday after
sired number of holidays
IBILIKI0I4I2I
•g
■0
CETJTRAL UNIT AND CENTRAL CONTROL
old water to
Supply temp,
induction un
At outdoo
temp, lim
ALT. 1
AF CR PC HS CHP
n principle built up according' to alternative No
ALT. 2
r T
«HiH!KM
T4 T1 T3 N + k'j T5 71 N+Jj T4 T5 T1 N+L'j
r T
ALT. 3
AF CR PC HS CHR
r T
L J
AF
"Anti-freese" coil, if any
CR = Cooling/Heat recovery coil
PC = Preheating ceil
HS = Sep. humidifying section
Temp, cf primary air at T1 Winter
If morning boost heating: Allowed
max. temp, of primary air at T2...
If "anti-freeze" coil: r
Mi;i. air temp, after coil (at T4)-...*fL
HEAT RECOVERY
Mark with 1 if:
"Dry" recovery coil.
Temp, efficiency of cooling/heat-
recovery coil ("dry" coil value)
if dimensioned principally with
regard to recovery function
Degree of humidificatic
•0
Central reheater, if any
Fan
Reheaters, if any
At outdoor
temp, limit .
If alt.1 ,
Temp, of ,
r.tral reheating coil:
If alt. 2
after humidifying sect.
fter coil (at T3) "F
3: Mm. temp.
(at T5).
"Sprayed" recoveiy coil (Alt 2 if
omitting sep. humidifying section).
Temp, rise
fan .
0
Min. supply temp, of cold water
available to central cool, coil
summer if cool./heat-rec. coil is
dim. only with reg. to req. cool. cap. . "'^l^
45 V
IF IHMER ZONES SHALL BE CALCULATED
Total air supply
to inner zones . . .
Number of working days per
Reheating temp, (at T2) fo
Shaded squares need not necessarily be filled in. When left open plausible data are put
the cor.puter. Blank (unshaded) sqiiares should aluays be filled in.
Pig. 3 "Common Plant Data" form for the four-pipe induction system program
401
SHADOW BOUNDARIES IN AUG ON ZONE 9 BEARING 166.0 DEGR.
- = SURFACE
" = SURFACE
ELEMENT
ELEMENT
IN
IN
SHADOW
DIRECT
OF NEIGHBOURING
SUN
BUILDINGS
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_______xx_
Pig. 4 Calculated boundary of moving shadow
402
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403
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Pig. 6 Result of calculation of central cooling plant
404
standardized Method for Optimizing
Building Construction and Heating
and Ventilating Installations for
Various Indoor Climate Criteria
by Arne Boysen and Sven Mandorff
The National Swedish Institute
for Building Research
Heating and ventilating Installations are used to create and mainta.in certain
room temperatures under variable internal and external heat loads. If these room
temperatures can be calculated for a given building, taking into account the thermal
properties of the building, the calculations may be used as a tool for an optimal
design of the building as a whole. It will be possible to choose between a building
with a high thermal storage and relatively simple heating and ventilating installations,
or a light building with more complex installations.
Such calculations are sometimes made for extreme climatic conditions. Those
conditions are, however, not representative of the accumulated heat stress during a
long period of time, and calculation cost or time does not allow a greater number of
calculations. A method will, however, be presented whereby a few calculations make
it possible to judge the resultant high room temperature over a period of one month.
The method is applied to classrooms.
In a building code this method can be used to regulate the heating and venti-
lating Installations. It is, however, then necessary to standardize most of the
factors that go into the calculation and only vary those factors which have the most
direct influence upon the design of the heating and ventilating system. It is also
necessary to find a simple rating of the room temperatures, so that comparisons of
different solutions will be feasible. This rating will be presented in addition to
a few calculations showing some, typical results. This paper is based upon part of a
research project, which has been published as Report 50/69 from the National Swedish
Institute for Building Research [l^ ' . A more detailed report, also giving results
of calculations according to the method described in this paper, will be published
in the near future.
Key V/ords: Building construction, classroom, duration of heat stress,
heating and ventilation, indoor climate criteria, optimized design,
performance requirements, room temperature.
1 . Factors Affecting Room Temperature
Room temperature may be affected by many different factors. The correlations are perhaps shown most
clearly by a diagram where the factors can be arranged in four different categories; i.e. internal loads,
external loads, building and installations.
B
Internal loads are normally heat emission from persons, lighting, machines and equipment. The
internal loads for the type of premises to be discussed here - namely, ordinary classrooms - consist
mainly of heat from pupils and teachers and heat from lighting.
Figures in brackets indicates the literature references at the end of this paper.
405
External loads are solar heat, transmission losses or transmission gains, influence due to the
dependence of the ventilation system on wind conditions and so on.
The influence of both external and internal loads is affected by the building through, for example,
its orientation, size of windows, thermal insulation etc. The heat storage properties of buildings are,
however, at least as important; heat is stored, for example, in the structure of a building and in its
furniture, fittings and fixtures. The volume of air stores air pollutants but also to a certain extent
heat. The damping effect exerted by a building is thus in part fixed once and for all by the method of
construction and the site, but can also vary, for instance, according to the use of adjustable sun
shading devices and opening of windows.
However, the range of variation possible in a building is as a rule not sufficient to be able to
compensate completely for the variations which occur in loads. The final compensation must therefore
come from installations, in this case heating and ventilation systems.
2. Calculations of Room Temperature
The traditional method of calculating the requisite thermal effect of these systems is to take
account of external loads, the building itself and an assumed room temperature. The heat flow is assumed
to have attained an equilibrium, and it is further assumed that the values of the factors included in
the calculations are not dependent upon time. This method involves great simplification of actual
conditions, simplifications which can possibly be accepted for calculating the requisite heating effect,
but which cannot be accepted for calculations of the necessary means of controlling temperature, or for
calculation of the required cooling effects.
In the case of these calculations the internal loads, the dynamic variation in these loads and the
effect of the building must be taken into account. These calculations are complicated and time-consuming.
In the normal sequence of calculation it is, however, possible to make simplifications of varying extent.
Different experts have suggested different simplifications, with the result that we have today a large
number of different calculation methods to choose between. The simpler methods are suited to manual
calculations, but the more detailed require computers. One problem is that different methods yield
different values and it is hardly possible to find such simple correlations between methods that results
from different methods can be converted and thus permit full-scale comparison. A method proposed by Dr
Gosta Brown j]2^ of the Royal Institute of Technology in Stockholm was used for the calculations in this
paper. This is probably one of the most com.prehensive methods and provides excellent scope for computing
most of the data which can be required for estimating the temperature of a room.
The way in which people react to the temperature of a room is partly conditioned by personal
preferences and partly influenced by other factors, - for instance, clothing. Apart from this it is
primarily three factors, air temperature, surface temperature and air velocities, which play a significant
part. Speeds of air currents are, however, low and hardly possible to calculate. An estimate of the
temperature of a room - the operative temperature - is therefore based on the prevailing surface and air
temperatures.
In the case of the temperature levels dealt with here, heat exchange between a person and his
surroundings is generally assumed to occur as much by radiation as by convection. This means that the
mean between air temperature and the average surface temperature of walls, floors and ceilings can be
taken as the operative temperature of the room. In calculating the average surface temperature, the
temperatures of the respective surfaces are weighed in relation to their solid angle, meaning that the
average surface temperature varies from point to point within the same room.
Thus the original diagram can now be modified as follows;
where
air temperature
different surface temperatures and
where K
the operative temperature
406
3. Relevant Point and Time
The importance of taking into account the point in the room to which the temperature estimate refers
is Illustrated in figure 1 . The diagram shows conditions in the vicinity of windows whose surfaces
usually show the greatest temperature deviation from the others. The part of the body facing a window
does not experience the same operative temperature as the part facing away from it. The scale of
temperatures gives the difference between these values.
The difference near to the window may be as much as 2°C, while at the wall of the room farthest
away from the window it is almost non-existent. A difference in operative temperature of approximately
1 °C is thus possible between these two points, which in view of the variations permitted in room
temperature is quite considerable.
Despite the fact that there may be considerable differences in temperature between different points
in a room it may be possible to disregard this complication when computing room temperature. In such a
case the temperature of a point in the inner part of the room is calculated. Whether the value obtained
will have to be adjusted for other points need only be considered when the result is to be assessed.
Even with due consideration for the points of view which have been put forward, this is not
sufficient to render calculations of room temperature meaningful. We must also be careful to decide for
which time calculations are relevant.
If calculations are to be used for dimensioning of air conditioning systems, they should, of course,
refer to the occasions which make the greatest demands on the heat removal capacity of the system.
However, the problem is as a rule somewhat different in schools. There, it is hardly a question of
complete air conditioning but of trying to achieve a reasonably comfortable room temperature by other
means. It is true that we may also wish to knov; the maximum value, i.e. the highest temperature likely
to occur, but discomfort is also a question of duration. It Is, for example, then possible to choose
between calculating the frequency for days with different maximum temperatures or the true duration of
high temperatures in hours.
The latter alternative is probably a better measure of the discomfort which occurs; i.e. in this
case, deterioration in the performance of the schoolchildren.
4. Results of Temperature Calculations on Sunny Days
We want to show some example of results of calculations of room temperature as a function of
different parameters. The calculations were made for a sunny day in May at the same latitude as Stockholm
assuming a room facing due south and with an average outdoor temperature corresponding to the average
for the whole month. This date v;as chosen in view of the fact that the school year finishes at the
beginning of June and that climatic conditions In May are therefore of particular importance.
The calculations are, of course, also dependent upon many other factors but since the aim is in
this case to present the method rather then the results, these factors have been omitted from this paper.
The influence of the structure is shown in figure 2. Case T represents a building with a high degree
of heat accumulation; external walls and floor slabs are of concrete, internal walls of double plaster-
board panels enclosing a layer of mineral wool. Case M is a building in lightweight concrete and case L
a timber structure having mineral wool as thermal insulation. All the alternatives represent entirely
normal constructions.
Figure 3 shows the effect of the size of windows and sun shading devices in a lightweight concrete
building; window sizes were 4 7 and 10 glazed area (double glazing) and as sun shading devices
Venetian blinds between the panes or curtains on the inside were assumed. Compared to the solar heat
gain through unshaded double-glazed windows, these arrangements admit 40 % and 60 fo respectively.
The curves in this diagram are not entirely comparable if, for example, the minimum requirement is
300 lux at the desks with the poorest illumination. In some of the cases this value is not attained
unless the lights are switched on. In rooms with the smallest window size fitted with Venetian blinds
the lights must be left on all day which raises the corresponding curve so that it almost coincides with
that for the largest window with Venetian blinds. With curtains the lights need only be on for an hour
in the morning and the paradoxical result is that a less effective sun shading device gives a lower
room temperature. This result is, however, not generally valid; it is a consequence of the special
conditions which were assumed to prevail.
Figure 4 shows how different ventilation systems can affect room temperature. The building has a
structure of lightweight concrete and windovjs with an area of T fitted with Venetian blinds (F^ = 0.4).
The five curves represent three different rates of air flow; 7-5 ""Vh per capita, 1 5 "'•Vh per capita
and /h per capita, combined with supply air of different temperatures, the lowest temperature being
407
limited to + 20°C, or + IS^C, or outdoor temperature without a lower limit. The conditions thus illustrate
a number of interesting cases. The rate of air flow of 1^ rn'/h per capita is more or less the rate
required according to current Swedish regulations. 7.5 ^/h per capita is approximately the rate that can
be expected in the case of many simple systems without mechanical ventilation or possibly with only an
extract fan. 30 ni'/h per capita is the rate attained using ventilating equipment which is specially
designed for classrooms. In the latter case it is possible to supply air with a minimum temperature of
+ 15°C without risk of draughts; with the simpler systems air is supplied without preheating and thus
without minimum temperature. In addition, central air conditioning plants are to be found; these supply
air to classrooms at room temperature, i.e. ca. 20°C, provided that the outdoor temperature is not
higher.
The last type of system mentioned has a poor cooling effect and induces high room temperatures. The
simplest system {7-5'^ per capita) would seem to be better, but this is a consequence of the conditions
regarding outdoor temperature which were assumed for the calculations. As soon as the outdoor temperature
rises a degree or two the simplest systems will give the highest room temperatures.
5. Calculating for Longer Periods
The results published apply for school hours during just one day. These results, though limited,
have of course a certain interest but in the majority of cases the prime aim is to extend the analysis
to cover longer periods of time. This can also be done by determining for each day of the period the
values of the calculation factors that tiave to be used.
Among the external factors it is primarily the temperature and the solar energy which vary. In the
case of the internal factors the use of classrooms and the number of persons varies. As for the
structural factors, it is conceivable that the use of the sun shading devices might vary or that windows
might be opened.
However, it is not sufficient to know how each factor varies individually; the simultaneous
variation must also be known. Since correlations do not always exist between the factors, it is
impossible to try to find a logical pattern in the covariation of all these factors and it therefore
becomes necessary to make certain simplifications.
V/ith regard to sun shading devices, it is reasonable to assume that these are always used when the
windows are sunlit during school hours, since this assumption is easy to handle mathematically and since
it is impossible from the practical point of view to maintain a reasonable room temperature on any other
grounds.
Opening of windows gives as a rule better ventilation and a lower room temperature. On the other
hand, v;ork in the classroom is disturbed by noise from outside and for this reason airing of rooms by
opening windows cannot be relied upon as being a generally acceptable method of controlling room
temperature. It is therefore reasonable in the case of the calculations we wish to make to assume that
windovjs are closed during lessons. During breaks, however, they are assumed to be opened to reduce the
room temperature.
The use of classrooms is of course governed by a time-table and this may mean that on certain days
a room is used for a smaller number of school hours than on other days. The trend, however, is towards
an increasingly intensive use of rooms and minor variations or displacements do not affect the room
temperature to any great extent. It is therefore safe to assume that in the case of these calculations
the daily schedule has not been changed. Similarly, it may be assumed that the number of persons present
in the room is the same from day to day.
Thus outdoor temperature and solar energy remain, for both of which extensive meteorological
statistics are available.
The mean temperatures per 24 h for four places over a period of thirty years are more or less
normally distributed for each place vjlth a standard deviation of ca. 3.5°C for months which are of
interest in this context as shown in figure 5. The same would appear to be generally applicable. We have
at any rate found that the monthly means of JO places chosen at random vary considerably, but that the
standard deviation lies between J.O and 4.0, Thus, using the monthly mean as a basis and having fixed
the standard deviation at J.S'C, it is possible to predict the average numbers of days that will have
higher temperatures. A still higher degree of precision can be obtained if the prediction is based upon
the temperature which represents the true standard deviation above the monthly mean temperature (Fig. 6).
As in the case of temperatures, differences exist between different times of the year and different
places for solar energy on clear days. Furthermore, differences in room orientation must be taken into
account. The difference for the same place and orientation are, however, not very great over a limited
period of time (Pig. 7).
If we examine the simultaneous variation of outdoor temperature and solar energy, we find that the
408
daily variation in the temperature Is greater on sunny days than the average, and that high daily mean
temperatures seldom coincide v;ith maximum radiation of solar energy. When temperatures are more than one
or two degrees higher than the monthly mean we can estimate the solar energy to amount to 8O-85 % of the
maximum value. [^5 J
Tiie position is thus in brief as follows:
1 . High classroom temperatures may be anticipated when a high outdoor temperature coincides
with solar radiation.
2. The high outdoor temperatures have a frequency corresponding to normal distribution.
3. At these high outdoor temperatures solar radiation on clear days is approximately 8O-85 io
of the maximum radiation.
These correlations make it possible to obtain a good idea of the duration of the high room
temperatures which can be expected by calculating the room temperature for the current outdoor
temperatures and then weighting the results according to frequency. Each outdoor temperature is given a
weight corresponding to normal distribution with a standard deviation of 5.5.
As many as 8-10 outdoor temperatures may be current at any one time. The total calculation volume
is thus considerable. It can, however, be reduced by utilizing the fact that the correlation between
outdoor temperature and the room temperature on the whole is linear. It is then sufficient to make, for
example, three calculations and to interpolate and extrapolate the remaining values, figure 8.
6. An Aid to Construction
This method can now be used as an aid in the construction of school premises. It is possible to
establish the temperatures that will occur at different orientations, the effects of the structure and
the building materials and the effect of different heating and ventilation installations etc. (fig. 9).
It is thus possible to make a completely objective choice of the combination vjhich yields the best
results. If the costs of the different alternatives are also included we can judge which will be the
optimum solution from the point of viev; of building costs.
The different results obtained from the calculations show quite clearly that different structural
factors can exert just as great an influence on room temperature as different heating and ventilating
installations. We realize that it is futile to try to guarantee a good room climate solely by drawing up
standards for installations. This point has also been proved practical in a large number of schools built
in recent years. It is possible, though nowadays hardly economically motivated, to concentrate entirely
on structural measures for controlling room temperature. Installations are essential and with the
calculation demonstrated it is possible to adapt them according to the building in question. The method
thus provides us v;ith a means of making demands on the room temperature and from these demands derive
the conditions for the installations. We have thus the chance of establishing highly functional
standardized rules for performance requirements regarding heating and ventilation systems. Such a rule
has been suggested, stating that "The classroom temperature, calculated according to this method, may
exceed 25°C during, as a maximum, 20 ^ of lesson time in months of May".
7. Functional Standard for Heating, Ventilating and Air Conditioning Plants
Such standardization can hardly be considered without first including model values for all the
factors wherever possible. Some of these values have been already touched upon, but not all of them. It
goes without saying that the model values must be chosen with great care; they must be realistic for
modern schools and modern work routines in schools, while at the same time deviations from the model
values may not produce excessively large deviations in the final results. Nevertheless, however much
care is taken deviations cannot be entirely avoided.
Here we should like to draw attention to one such deviation. As v;e said earlier, the statement made
regarding the curve showing normal distribution for outdoor temperature is based on statistics from the
years -. This applies then for a long period of time but not necessarily for individual years.
This means that in certain years the high outdoor temperatures may have longer duration, causing the
high room temperatures also to last longer than intended. Conversely, it is possible to obtain shorter
values. In other words, there is very little chance of checking in an existing building, if the standard
is fulfilled. The standard will be purely for purposes of calculation.
It may be acceptable from the point of view of the community that a standard of this nature in the
long run should give reasonable temperature conditions. For the individual pupil, however, this is un-
satisfactory as he or she may be spending only one year in the classroom in question.
This weakness, if indeed it is to be regarded as such, would appear to be inevitable. It is, however,
possible to prevent the most unsuitable conditions through choice of temperature limit or duration value
in the standard.
409
Thus, In this case it is possible to use computer techniques for a standard concerning heating and
ventilating installations in classrooms which is functionally constructed in that it adopts the
permissible room temperature as a basis and compels us to take into account the thermal properties of
the building and the purpose for which the premises are to be used. This standard is probably the first
of its kind and should represent a great step forward in comparison with other regulations applied to
date which have been proved largely incapable of preventing unsuitable classroom temperatures.
8. Literature references
[l ] Antoni, Nils, Pro jekteringsunderlag for skol-
byggnader for grundskolan, Statens Institut
for Byggnadsf orskning, rapport 5O/69.
|^2j Brovm, G., A method of calculating heating and
cooling loads v;ith the aid of a digital
computer. WS 54 () No. 11.
[5J Adamsson, B. , I968, Val av klimatdata vid be-
rakning av hogsta rumsluf ttemperatur och even-
tuellt kylbehov, Tekniska Hbgskolan, Lund.
Institutionen for byggnadskonstruktionslara.
Arbetsrapport :5.
DIFFERENCE IN OPERATIVE TEMPERATURE
•c
3
2
1
0
^/.56
Figure 1 DISTANCE FROM WINDOW m
Difference in operative temperature (between two opposite directions) as a function of the distance from
windows and glazed area. The values have been calculated on the assumption that the difference between
the temperature of the glass and the mean of the room air and the temperature of the interior surfaces
is 5. 10 and 15°C respectively. Cases a, b and c show the conditions for different sizes of window (A =
= 4 m^, 7^1^ and 10m^).The point of reference lies on the centre line in relation to the window and on a
level with the lower edge of the window.
LESSON TIME
20 21 22 23 Ik 25 26 'C
P^g^^^ g ROOM TEMPERATURE
Duration of room temperature during lessons in classrooms in neavy IT), medium-heavy (M) and light (L)
structures; the prerequisites are among others a sunny day in May, due south orientation of the room and
the same latitude as Stockholm, Daily mean temperature + 1 1 °C.
410
LESSON TIME
%
20 21 22 23 2U 25 "C
ROOM TEMPERATURE
Figure 3
Duration of room temperature during lessons In classrooms with different sizes of v/lndow (A) and sun
shading arrangements (F 1); the prerequisites are among others a sunny day in May, due south orientation
of the building and the same latitude as Stockholm. Daily mean temperature + 1 1 °C,
LESSON TIME
%
20 21 22 23 2U 25 26 'C
ROOM TEMPERATURE
Figure 4
Duration of room temperature during lessons in classrooms with different rates of air flow and supply
temperature; the prerequisites are among others a sunny day in May, due south orientation of the room
and the same latitude as Stockholm. Daily mean temperature + 1 1 °C.
411
DISTRIBUTION OF 2^h PERIODS %. .
Figur e 5
Frequency of different daily mean temperatures
during the period -. The values refer
to four towns and the months of May (5) and
June (6).
0 2 ^ 6 8 10 12 U 16 18 20 22 2L 'Z
MEAN TEMPERATURE PER lU h
Figure 6 12° 16° 20°
Isotherm map for May. The isotherms refer to the mean monthly value of the outdoor temperature + the
standard deviation in the daily mean temperature.
412
kcal/24h
Oj , . \ , . ^
±180 ±120 ±60 0 ±60 ±120 ±180
ORIENTATION
Figure 7
Heat gain from direct and Indirect solar radiation through an unshaded double-glazed window. Values are
given for two towns, one In southern- Sweden and one In northern Sweden. The diagram is valid for the 15th
day of each month, ground reflection r = 0.25.
TIME %
20 21 22 23 2i, 25 26 27 28 29 30
ROOM TEMPERATURE 'C top
% OF TOTAL LESSON TIME
Ol . , ? , . . ^
20 21 22 23 2i 25 26 27 28 29 30
C top
Figure 8
Duration of room temperature during lessons at different values of the daily mean of the outdoor
temperature. The lower part of the figure is a sum of the curves in the upper part, account having been
taken of the relative frequency q ^ of different outdoor temperatures. Prerequisites are among others
sunny days in May, due south orientation of the room and the same latitude as Stockholm.
413
TOTAL LESSON TIME
^0 r-^^ ,
30
23 2^ 25 26 27
ROOM TEMPERATURE 'C
Figure 9
Duration of room temperature in classrooms with different combinations of structure and ventilation
systems. More or less the same results are obtained in a lightweight building with an air flow of ^0 n'/h
per capita as in a medium-heavy building with an air flow of 1 5 "^'/h per capita. Prerequisites are among
others sunny days in May, due south orientation of the room and the same latitude as Stockholm.
414
Designing Installations by Computer in Sweden
1
Lasse Sundberg
Wahlin'g's Installation Development Company
Stockholm
Sweden
Designing buildings and their installations has become more complicated.
The building-time is shorter now than earlier because of improved building-
methods. Increased demands for exterior and interior environment and more
sophisticated installation equipments will increase the demands upon the de-
signer. To make it possible for. him to follow this development he has to
use effective means of assistance. The computer can offer the designer this
help, but first after a wide development work.
In the National Swedish Council for Building Eesearch commissioned
us to investigate the possibility for rational designing of installations
by computer. The purpose of the investigation was to make an inventory of
existing computer programs, to analyse and systematically compare them and
give recommendations for the continuance of the work of development. The
investigation showed that there are computer programs only for some routines
of calculation. However they are made in a way which makes it difficult to
use them practically for designing. The programs are written in different
languages. There are also no standards for forms and documentations of
programs. Due to this investigation the coming work will be concentrated
on working out a basis for rational applications of data processing. The
work will be done with grants from the National Swedish Council for Building
Eesearch according to the following principles:
- A data coordination group for the building trade, including the
installation trade, has been appionted in order to investigate which program
language is giving the best qualifications for a flexible use of new programs.
Rules for description of programs, disposition of forms, presentation of
results and so on will be drawn up.
- On the basis of the recommendations of the coordination group the
calculation routines for designing installations will be programmed. This
work has already begun by collecting theoretical formulas etc. We shall also
investigate the possibilities how to use the computer for choosing instal-
lation components such as fans, pumps, boilers, valves and so on.
Key Words: Computer program, designing, electrical installations,
environmental engineering, installation in buildings, mechanical
installations, sanitary installations, Sweden.
1. Introduction
It is becoming more and more complicated to design buildings and the installations that go
with them. Construction takes place more rapidly because of improved building methods. Future
buildings will probably require even more installations, and more advanced versions of them,
because of the increased demands that are being made on the indoor and outdoor environment.
Equipment installed today must be capable of future modernisation or replacement, within the use-
ful life of buildings as a whole, because of the rapid development that is taking place in the
field of installation systems and products.
1
Mechanical Engineer
415
The above factors make great demands on the planning and construction of installations, and
will continue to do so. It is now more than ever necessary to plan well in advance, to make preli-
minary investigations and to carry out trial calculations to compare alternative systems with each
other in terras of installation and running costs. Naturally comparison should also be made with,
other possible technical solutions, based on different layouts or methods of construction. The
technical and economic calculations involved in planning a comprehensive and complex projekt can-
not usually be carried out with the help of approximate formulae, diagrams and slide-rules alone.
For these purposes computer techniques should be exploited to the full.
In the National Swedish Council for Building Research commissioned us to investigate
the possibility for rational designing of installations by computer. The investigation was car-
ried out with the above background. The aim was to make an inventory of the computer-based
methods that are currently applicable to the planning of installations, and to suggest ways in
which they could be developed. The results may be found in a report (I) that has been published, the
contents of which are summarized in this paper. The investigation showed that there are computer
programs only for some routines of calculation. However they are made in a way which makes it
difficult to use them practically for designing. The programs are written in different languages.
There are also no standards for forms and documentations of programs. Due to this investigation
the coming work will be concentrated on working out a basis for rational applications of data
processing.
2. The Available Choices of Machine
The choice of machine depends firstly upon which program or programs are available for the
purpose. Programs owned by other users are often linked to some special type of machine, or even
to a certain machine. It is usually possible to obtain the use of programs stored at other data
centres.
Programs whose development has been supported by the Building Research Council are at pre-
sent available without cost. The user must pay for the machine time that he uses in running the
program. Certain non-recurring costs can be involved in adapting the program for use at the
chosen data centre. The following choice of machines is available:
1. Rent of machine time at data centre.
2. Rental of a small machine.
3. Terminal of teleprinter type.
The various alternatives are discussed in more detail in the report. It is thought, however,
that alternative 3 will prove to be the most useful, in the majority of cases.
3. Rationalisation using Computer Techniques
In the planning of installations calculations must be made at the various stages of construc-
tion. Shortage of time often leads to the acceptance of values based only on personal experience
as the basic criteria for various judgements that have to be made. Approximate formulae and rules
of thumb are often allowed to serve in place of exact calculation.
Such short cuts are often satisfactory, but they seldom allow alternative interpretations.
What influence would different solar screens or differently constructed windov;s have? How would
the air heaters and their control systems behave under different loads? What different lighting
effects would be achieved by combining three different types of lighting element with four diffe-
rent floor coverings in a landscape office? How vjould the choice of ventilation system affect the
heat dissipation from the light fittings? Naturally these questions can be ansv/ered by manual
calculation, but the necessary time is not usually provided in the schedule. Computer techniques
make it possible to weigh the different alternatives against each other, often for considerably
less than it would cost to have the calculations for a single alternative made by an engineer.
It is true that calculations can be made quite rapidly with the help of tables and nomograms but
these are always based upon certain constants that cannot be changed without drav;ing up a comple-
tely new table or nomogram. Changing conditions can render such constants inapplicable, but the
necessary changes are seldom made. The constants in a computer program can easily be changed,
which makes data processing by this method more flexible. Experience has shown that builders and
architects quickly realise that automatic data makes a more subtle analysis possible, even if they
have originally been sceptical.
Few programs that are both suitable for the present purpose and intended for use via a data
terminal are as yet available. Most of the available programs are very large and ambitious. Some
of them are also closely linked to a certain type of machine. A number of computer manufacturers
are interested in producing a "packaged program" for use via data terminals. For this to be rea-
lised, private users will have to make their programs available and further programs will have to
be specially written for use via data terminals.
416
Existing programs
Several programs are currently available for
programs written for the purpose of research, whi
inventory of programs in Scandinavia, in order to
rams and their possible areas of use. They are de
engineers a summary they can easily use.
The programs described in the report are
is given in parantheses.
the planning of installations. There are also
ch could be adapted for practical use merely by
give a systematic overvievj of all these prog-
scribed in a simple v;ay in order to give design
listed below. The author or ovmer of each program
a. Room Temperatures; Cooling and Heating Loads
Calculation of cooling and heating loads for a building and design parameters for comfort
ventilation systems (AB Svenska Flaktf abriken) . - The program calculates the loads for one module
and one hour based on a sunny day and a cloudy day for each month of a metheorological normal-
year and also for an extreme day in summer and in winter. The calculations are not bound to any
special comfort system. The influence of moving shadows are also calculated.
Calculation of room temperatures (AB Svenska Flaktf abriken) , - This is a similar program to
the first, but no cooling of the air and also no supply air flow can be simulated.
These two programs are presented in a separate paper by W Boeke.
Calculation of room temperatures and of cooling and heating loads (G Brown, KTH). - This
program calculates for one or more rooms during em arbitrary period of time, one quantity of
each: cooling and heating load, room temperature, sufficient air flow, temperature of supply air.
Max and min values can be given to one or two of the quantities. This is a research program and
intended to be very flexible. It is presented in a separate paper by G Brown.
Calculation of room temperatures (C Allander, E Abel, KTH). - The program calculates the
room-temperature in a multi-room building. It is limited to rooms with a facade wall and mecha-
nical ventilation and is designed for the summer period in the southern and middle parts of Swe-
den, especially Stockholm. The program is based on a method, described in the ASHRAE Guide and
Data Book , p. ^^9-30^.
Calculation of room temperatures and cooling and heating loads (Richard Nilssons Konstruk-
tionsbyra AB) . - The program calculates the room-temperature, airflow, air inlet temperature,
cooling and heating load for one or more rooms in a building. The calculation is made for each
hour in ajiy chosen month. The input data can be chosen freely. Either can the cooling load be
calculated from a certain airflow, or the airflow can be calculated from the cooling load. The
calculation can also be done with regard to the influence of moving shadows. The outdoor tempera-
ture is approximated to a sinus function.
Calculation of cooling and heating loads and of the energy requirements of a building
(Ekono, Finland). - A series of programs have been developed by the Finnish company Ekono. One
program calculates the heating load with regards to the wind pressure and unwanted ventilation.
This program is described in JIHVE, March , p. 357-368. Two programs calculate the cooling
and heating load respectively the energy requirement. They are described in the ASHRAE Journal,
Sept. , p. 63-68.
b. Temperatures in Structures
Calculation of temperatures in a structure of parallel layers (B Ludvigson Ingen jor sbyra AB)
The program is calculating the variation in temperature in a structure, consisting of parallel
layers. The temperature on each side of the structure must be known, either constant or as a
function of time. Maximum 15 parallel layers can be used. For each Iciyer the temperature in the
center is calculated. The program is specially written for testing different kinds of insulation.
Calculation of temperatures in a cross section of an arbitrary structure (Industridata AB).
This program is calculating the temperature in a structure and the layers need not be parallel.
The heat flow can be constant or suddenly changing. A heat source within the calculated zone is
allowed. The border of the zone and the heat transfer coefficient may be a linear function of
time. It is useful for complicated constructions.
417
c. Heating Systems
Calculation of the design parameters for one and two-pipe heating systems and their distri-
bution netv;orks (AB Databerakning) , - The program calculates the type and size of the radiators,
the pipe dimension, the friction loss, the valve dimension and the size of the distribution pump.
A quantity list including all prices can also be calculated. Any make of radiators can be used.
The program is useful when deciding the hot water temperature, the pipe dimension regarding
energy consumption etc in order to find the lowest annual cost.
Calculation of the design parameters for single-pipe heating systems (Fellingsbro Verkstader).
The program calculates the size of radiators, valves, pump and a quantity list. The heating load
can also be calculated. The program is specially designed for radiators made by the company
Fellingsbro, Sweden.
d. Water-pipe Networks
Calculation of the pressure and flow conditions in a network of water pipes (Industridata AB) .
The program is simulating a distribution network, e.g. a part of a town. The pressure and the
flow for every connection in the netv/ork is calculated for a certain moment. Alternative con-
sumptions of water can be simulated, as well as alternative data for pumps and reservoirs.
e. Waste-pipe Networks
Calculation of flow conditions in a waste-pipe network (Industridata AB). - The program is
designed for a rather large network. The flow is calculated as a function of time, depending on
the flow on every terminal point.
f. Stress in Pipe Systems
Stress calculations for pipe systems (Industridata AB). - The program calculates deformations,
loads and stress forces in a pipe system due to temperature alterations, inside overpressure, dead
weight, concentrated forces and moment, forces from flow of fluids, and forced deformations. The
network system is supposed to be anchored in one or more points, with or without springs or sli-
ding support.
Stress calculations for pipe systems (IBM). - The program calculates the pipe system based
on an electrical analogical method and gives forces, moments, distorsion and stresses in diffe-
rent joints. No respect is taken to dead weight or the forces from flow of fluids.
g. Ventilation Systems
Calculation of the design parajneters of a ventilation system for constant static pressure
(Wahlings Konstruktionsbyra AB) . - The program sizes ventilation duct systems based on the con-
stant static pressure method. Duct types, dimensions etc are given in tables. The program calcu-
lates loss of pressure from the fan to each section and static regain. Friction loss can also be
calculated only regarding to highest air speed.
Calculation of the design parameters for ventilation systems (AB Svenska Flaktf abriken) .
The program sizes ventilation duct systems regarding to less sheet area and most possible even
pressure over air inlet or air outlet. The fan pressure can either be calculated or given as
input. Necessary dampers are calculated. A quantity list can also be printed.
h. Heat Loss from Pipes
Calculation of heat loss from pipes, flooring or ground (Hugo Theorells Ingenibrsbyra AB).
The program calculates the heat emitted from hot water pipe loops embedded in concrete, sand etc,
for floors and pavements. The prograin can also calculate the necessary heat for melting the snow
on pavements.
i. Viscous Resistance
Calculation of viscous resistance in pipes (Hugo Theorells Ingeniorsbyra AB) . - The program
calculates the flow, the speed, the dynamic pressure and the friction loss pr lenght unit for
any desired diameter and fluid in a pipe. The result is given in tables.
418
k. Sun, Shadow, Lighting
Irradiation from sun and sky in Sv;eden on clear days (G Brown, E Isfalt, KTH) . - The program
is calculating the irradiation together with the position of the sun in the sky for each hour
from sunrise to sunset on a clear day. The radiation transmitted through horizontal and vertical
double-glazed windows and the irradiation onto horizontal and vertical surfaces are also calcu-
lated.
Calculation on shadows moving across building facades (G Brown, E Isfalt, KTH). - The prog-
ram calculates for any desired time on a sunny day the shadow on a facade, caused by narrow buil-
dings or other objects. The facade is divided into an arbitrary number of squares, thus giving a
picture in scale of the facade. The shadowed squares and the contour of the building are printed.
Calculation of the light distribution in a room (G Brown, E Isfalt, KTH). - The program cal-
culates how the irradiation in the state of diffused light is distributed in a room. The light
source should be a part of a wall, e.g. windows and built-in fluorescent tubes. The irradiation
is given for a small area, the position choosen freely in the room.
1. Electrical Networks
Calculation of radial high and low voltage networks (Industridata AB) . - The program can be
used for continous control of existing radial high or low voltage networks or combined networks,
concerning potential drop, loads, fuses, response to sudden loads, short-circuit currents and
currents to earth. It is also useful as a simulation program when planning a new network.
m. Lift Usage Patterns
Simulation of lift usage patterns (Asea-Graham) . - This program can simulate lift (elevator)
usage in office buildings, hospitals, hotel, department, stores and other similar buildings. The
simulation is made by a simulator, special built for this purpose. Due to the number of floors,
persons etc the waiting time after a call for the lift is calculated.
5. Suggestions for Future Development Work
5.1 Supplementary Research
Programs v/ritten for research purposes could often be of great practical use for engineering
work. However, most of them require certain additions before they can be taken into practical
use, e.g. data forms, program descriptions and adaptation to different machines. This kind of
program development can most easily be done by the original author in consultation with design
engineers familiar v^fith the proposed area of use.
5.2 Continued Work
A Review of the various routines used when planning installation projects was also included
in the report. In view of this, a proposal for new programmes was made. Example of programmes:
Heat exchanger system. Chimneys (dust distribution), Two-way valve system. Heat loss in pipe or
duct network. Distribution of air within the duct system. Estimation of costs and quality. Opti-
mum planning of a plant, Calculation of control circuits.
6. Selection of Products by Computer
6.1 Data Terminals
The day will probably come when each installation consultant will rent a data terminal, that
is connected to a data centre via the network. In this way, with only a small capital
outlay, using the capacity of a large computer, one will be able to carry out very complicated
calculations'.
Details of the veirious products are needed continually during designing in order to facili-
tate selection of products. This information is generally obtained from catalogues and brochures.
It is often very difficult to find just the right product amongst such extensive material. Some
companies arrange their brochures in files; there is, however, a risk that some brochures are
either missing or have become obsolete. There are so many pages for some code indexes, that it is
impossible to check the complete details for each of the products.
419
6.2 Selection Methods
In order to make selection quicker and more accurate, data terminals can be used. This makes
it possible to find the right product via an automatic selection system.
In order to utilize such a system, which should be based on an interchange of information
between computer and designer, details of every product given by the manufacturer must be avai-
lable. These facts are keys to the selection system.
One condition for developing a selection system is that the user must be able to find his
product by freely specifying his requirements. He commences the dialogue with the computer by
giving a general classification, for example, "pump" or "valve". There must only be a few general
classifications to cover the whole range of existing products and any others that may be included
later.
The computer answers by supplying a list of the various sub-group, for example, "pump for
water", "pump for oil" or "manual two-way valves", "automatic controlling valve". The user then
chooses a sub-group. Thes,e sub-groups should be small but still it should not be necessary to go
through more than one of them in order to find the required product.
Once the sub-group has been decided upon the process of selection really begins. The computer
then lists the various characteristics of the products within the group. With the help of these
the user can select the features he wishes to specify. It can be details concerning size, material,
media, geometrical design, sound, standard, brand etc.
It is the computer that does the selecting all the time, by giving information about the par-
ticular characteristics of the vairious products.
Such a system of selection has to be very flexible. It must be possible to select a product
by carrying out a detailed dialogue as just explained, as well as being able to give merely the
sub-group and requisite features, in order to shorten the dialogue.
Any changes in the existing products or details of new products must be easily included so
that a manufacturer can immediately inform all the customers using the data terminals.
6.3 Handling of Information
The selection system leads up to an identification of the products fulfilling certain requi-
rements. The selection system does not include complete information about each product. However,
data techniques can even be used to help in this respect.
Three alternative methods for storing information entailing varying degrees of automation
will now be described.
a. Alternative 1
The information is stored as at present, in systematically arranged brochures and catalogues.
The selection system refers you to certain pages in the files by giving the code and name of the
product and the manufacturer. The appropriate pages are then picked out manually.
In this case the selection system facilitates the use of the files of brochures, besides
which you are informed of products not represented in the files. In this way the files on relevant
products are kept up to date.
It is only necessary in this case, to have a data terminal for calculation routines.
b. Alternative 2
The terminal users need no brochure collections of their own. Such files are only kept in a
pool, but in turn may be linked to a computer. All brochures are micro-filmed, thus enabling the
whole range of products and their various details to be stored conveniently in a number of micro-
film cartridges.
Every terminal user has a complete set of cartridges. He also has a so-called "reader-prin-
ter", i.e. an apparatus which enables one to get an instant reference view of any desired frame
on a large screen. Prints of the relevant pictures can also be produced within a few seconds.
The contents of all cartridges are reviewed and up-dated each year.
420
Any changes that occur during the year can be immediately put into a supplementary cartridge,
which is distributed regularly to all customers.
The selection system is adapted to provide not only the name and manufacturer of the product
but also to give information regarding the cartridge number of the frame in the cartridge. This
alternative entails a certain amount of capital investment and some operating costs, but at the
same time it cuts out the expense of producing and distributing brochures to all the terminal
users.
c. Alternative 3
The terminal user has no files at all. All information regarding products is stored centrally,
on video tape, microfilm or something similar, and linked to a computer.
The system necessitates selection by dialogue with the computer via the terminal. When selec-
tion has been completed, relevant frames are projected directly onto a screen after being trans-
ferred from the data centre via the telecommunication network. Prints can also be obtained when
required.
This system completely eliminates the risk of getting obsolete information, as any changes
can be made quickly and are immediately available to all users.
Capital investment and operating costs will, however, be considerable. Despite this, there
are a few such systems in the USA at present and there is a wide general interest in this type of
system. As a result manufacturers of data and telecommunication systems are carrying out intensive
research.
7. References
(l) Allan Westrbm & Teddy Rosenthal. Computer techniques for the planning of installations.
National Swedish Building Research, Report R1:-, 100 p.
421
A Cost Analysis Service Helps
Optimize Building Costs and
Environmental Benefits
John T. Malarky''"
PPG INDUSTRIES, INC.
Glass Division
One Gateway Center
Pittsburgh, Pa.
During the past decade architectural glass performance has
been improved to help achieve a comfortable indoor environment.
Lower shading coefficients reduce solar heat gain 75%. Lower U-
values reduce heat loss 6 5%. This performance results in cooler
indoor glass surfaces in summer, warmer indoor glass surfaces in
winter enabling easier system control and a more comfortable
thermal and visual environment indoors.
A Cost Analysis Service has been developed to provide a
direct cost comparison of the effect of improved fenestration on
overall building costs. This service, called Building Cost
Analysis, utilizes a computer program, cost estimates and rough
project design criteria early in the design stage to obtain a
first approximation of the effect of glass performance on construc-
tion and operating costs. This rough economic analysis obtained
before glazing and mechanical system design is firm, may indicate
that a more detailed professional study of glass selection best
suited to the needs of the project is warranted.
The program computes initial heating and cooling equipment
costs, annual heating and cooling operating costs and long term
owning and operating costs for each glass under consideration.
Two case histories, a two-story office building in Madison,
Wisconsin, and a 57-story office building in Columbus, Ohio,
illustrate the potential savings high performance architectural
glass products may have for the owner, greater design freedom for
the architect and for the engineer, summer and winter insulating
performance enabling more accurate control of the indoor system
creating a year-round comfortable environment.
Key words: Shading coefficients, U-values, approximation,
heating and cooling equipment costs, annual operating
costs, present worth, owning and operating costs,
potential savings, comfort.
Mechanical Engineer
423
A Cost
Building
Analysis Service Helps Optimize
Costs and Environmental Benefits
Building owners and managers who rent space to make money recognize that tenants
pay premium prices for offices with large window areas. They know also that sophisti-
cated control of temperature, air movement, humidity and radiant temperature within the
comfort range is a necessity in the high rent district. Glare, condensation and drafts
long have been associated with simple clear glass windows.
To meet these comfort needs new types of windows have developed and the computer
has been put to work to provide an objective means for comparing glass performance and
economics on specific jobs.
During the past decade architectural glass performance has been improved to help
achieve a comfortable indoor environment. Lower shading coefficients reduce summer
solar heat gain 75%. Lower U-values reduce winter heat loss 65%. This performance
results in cooler indoor glass surfaces in summer, warmer indoor glass surfaces in
winter enabling easier system control and a more comfortable thermal and visual
environment indoors.
A Cost Analysis Service has been developed to provide a direct cost comparison of
the effect of improved fenestration on overall building costs. This service utilizes
cost estimates and rough project design criteria early in the design stage to obtain a
first approximation of the effect of glass performance on construction and operating
costs. This rough economic analysis obtained before glazing and mechanical systems
design is firm, may indicate that a more detailed professional study of glass selection
best suited to the needs of the project is warranted. Also, because it relies on a
sophisticated computer program for processing and analyzing the data, it is quick and
easy to use.
The Building Cost Analysis service utilizes 38 data input items. The program
selects a summer and winter design day based on typical weather data for 30 geographi-
cal areas throughout the United States. Then, considering building orientation,
materials, construction, energy systems and heating and cooling methods, determines the
peak and annual heating and cooling loads. With this information, mechanical heating
and cooling equipment size is determined and annual heating and cooling operating costs
are estimated.
Also, the program uses estimated initial costs of the building, land, interest and
taxes to compute the present worth and long term cost of owning and operating the
building .
The Building Cost Analysis program is written in Fortran IV-G language and is run
on an IBM-360-40. The memory area required for the program is 140 K. Each run takes
approximately two minutes.
The program takes the input data (Chart I) , accesses the design program from
storage discs, calculates the latent (Design 1) and sensible (Design 2) heat loads thus
determining the peak heating and cooling loads. Next, it accesses the energy program
from storage discs and calculates the annual energy required for heating and cooling
loads. Then, for the type of energy used - all electric, electric air conditioning -
gas heating, all gas, the program estimates the annual heating and cooling operating
costs. Finally, the program computes the building present worth and the annual cost of
owning and operating the building.
The Building Cost Analysis program is designed to accept multiple runs for any
geographical area or building variable.
Since the program has been designed to investigate the effect of various
fenestration materials on buildings, glass performance is the variable we usually
compare. Other building parameters for a specific product usually are fixed from run
to run. The same program could be used to make other comparative analyses.
By introducing performance properties of alternate glasses, such as single clear
glass vs. single tinted glass or clear insulating glass vs. reflective insulating
glass, the program provides a direct comparison of the cost effect of these glasses on
building cost. The most significant difference usually occurs in the initial cost of
the mechanical equipment and the initial cost of the glass. Operating costs can be
significant too.
424
Two case histories illustrate the effect architectural glass in buildings may have
on initial and long term building costs.
CASE HISTORY #1
The first case history is a two-story building in Madison, Wisconsin. This
building consists of approximately 96,000 sq . ft. of rentable floor area. The proposed
building will be occupied by 450 people during the hours of 8:00 a.m. to 5:00 p.m.
Electric lighting will utilize 6 watts per sq . ft. Heating and cooling energy will be
all-gas. The building facade will be all-glass construction - vision and spandrel area
totaling approximately 15,000 total sq. ft.
The owner, architect and engineer selected three glass alternatives which were
compatible with the aesthetic design. The glass alternatives selected were: 1/4-inch
S0LARBR0N2E Plate, 1-inch LHR SOLARBRONZE TWINDOW (a fired-on reflective coating on
the air space surface of the outdoor glass in an insulating unit) and 1-inch
SOLARBAN (2) TWINDOW (an insulating glass unit with a metallic reflective solar control
coating on the air space side of the outdoor light) .
Table I illustrates the performance properties of the architectural glass alterna-
tives and the installed cost of the glass per sq . ft. (The installed cost includes
glass and installation charges) .
Table II illustrates the Building Cost Analysis results. These represent building
heating and cooling peak loads for each glass alternative. Note the improved
performance (insulating value) of the more sophisticated glasses results directly in
reduced heat gains and heat losses.
Table III is a summary of each glass alternative which includes the initial cost
of the glass, the heating and cooling system costs and the cost difference between one
glass and another. Initial cost comparisons reveal a potential savings of $15,000 if
the more sophisticated reflective insulating glass - the SOLARBAN were used instead of
the 1/4-inch SOLARBRONZE Plate. Thus, the owner and architect may elect to use the more
sophisticated glass product at no increased initial construction cost.
Table IV summarizes the Building Cost Analysis program output on the building and
shows that though the potential savings (initial and operating costs) are significant,
the present worth and owning and operating costs remain relatively unchanged. This is
typical when savings due to sophisticated architectural glass performance offset
increased glass costs.
The principals used this information as incentive to investigate architectural
glass alternatives more thoroughly. They elected to use the SOLARBAN product realizing
that in addition to the potential savings, the glass provided added comfort due to
warmer indoor glass surfaces in winter and cooler indoor glass surfaces in summer.
CASE HISTORY #2
The second case history is a proposed 57-story office building in Columbus, Ohio.
This building will consist of approximately 645,000 sq. ft. of rentable floor area;
3,000 people occupy the building from 8:00 a.m. to 6:00 p.m., electric air conditioning
and gas heat are the energy requirements. The building facade is approximately 56%
glass - 210,000 sq. ft.
The owner, architect and engineer selected three glass alternatives which they
felt were compatible with the building aesthetic design.
The glass alternatives selected were: 1/4-inch SOLARBRONZE Plate, 1-inch
SOLARBRONZE TWINDOW (insulating glass with the outdoor light tinted bronze) , 1-inch
SOLARBAN (2-3) TWINDOW (insulating glass with the metallic oxide solar control coating
on the air space surface of both indoor and outdoor lights) .
2
TWINDOW insulating glass construction consists of two lights of 1/4-inch clear or
tinted glass separated by a 1/2-inch air space and retained in a stainless steel
compression channel about the perimeter of the unit. Solar control reflective
coatings normally appear on the air space side of the indoor or outdoor lights.
(Figure 1)
425
Table V illustrates the performance properties of the architectural glass
alternatives and the estimated installed cost per square foot.
Table VI illustrates the proposed building heating and cooling peak loads for each
glass alternative. The improved performance properties of the sophisticated architec-
tural glasses result in reduced heating and cooling equipment requirements.
Table VII is a siammary of each glass alternative including the initial cost or the
glass plus the cost of the heating and cooling equipment. The initial cost comparison
reveals a potential savings of approximately $570,000 if the SOLARBAN TWINDOW were
selected over the 1/4-inch SOLARBRONZE Plate.
Table vni summarizes the Building Cost Analysis program output for the proposed
building and shows, in addition to the potential initial savings, an approximate $9,500
savings per year in heating and cooling equipment operating costs. Also, present worth
and owning and operating costs are shown.
The potential savings of over half a million dollars plus $14,000 per year in
heating and cooling operating costs encouraged the architect and engineer to enthusias-
tically conduct professional studies on the glass alternatives to demonstrate to the
principals' satisfaction that the potential savings through discriminate selection of
architectural glasses is realistic.
Often the Building Cost Analysis program shows that a potential justification for
use of more expensive sophisticated glass products leading to increased indoor thermal
and visual comfort is achievable at little or no initial cost to the owner.
"Potential savings" is used throughout because the results shown represent a sav-
ings of heating and cooling equipment based on estimated "installed heating and cooling
equipment" costs. Depending on the timing of a Building Cost Analysis, however, the
"achievable savings" may be somewhat less. Potential savings can be realized if the
architect and engineer conduct architectural glass studies early in the design process.
This service provides rough cost estimates early in the design stage to encourage
architects and engineers to conduct a professional design study of the economic
feasibility of sophisticated, aesthetically desirable architectural glass products.
The case histories illustrate the potential savings high performance architectural
glass products may provide the owner, the greater design freedom for the architect, and
for the engineer, summer and winter insulating performance enabling more accurate
control of the indoor systems creating a year-round comfortable environment.
The Building Cost Analysis program helps professionals relate an increased client
awareness of potential savings with sophisticated high performance glasses which may
lead to improved occupant comfort and satisfaction of the client's needs.
426
CHART 1 BUILDING COST ANALYSIS
BLOCK DIAGRAM
INPUT FROM
ARCHITECT
AND/OR ENGINEER
DESIGN
1
DESIGN
2
ENERGY
DETERMINES SIZE
OF HEATING AND COOLING
EQUIPMENT
DETERMINES ANNUAL
ENERGY REQUIREMENT
FOR HEATING AND COOLING
EQUIPMENT
FUEL
A
COST OF ANNUAL NNERGY
REQUIREMENT
PRESENT WORTH, ANNUAL COST
OWNING AND OPERATING A
BUILDING
OUTPUT TO
ARCHITECT, OWNER OR
ENGINEER
427
FIGURE 1 - TYPICAL TWINDOW CONSTRUCTION
428
MADISON BUILDING
TABLE I • GLASS ALTERNATIVES
DESCRIPTION*
U -
VALUE
SHADING
COEFFICIENT
INSTALLED
COST
S PER SQ. FT.
A. 1/4-INCH SOLARBRONZE PLATE
0.8
0.54
$ 1.25
B. 1-INCH LHR SOLARBRONZE TWINDOW
0.5
0.32
4.10
C. 1-INCH SOLARBAN (2) TWINDOW
0.30
0.16
3.60
*ALL WITH INDOOR SHADING
429
MADISON BUILDING
TABLE II RESULTS
DESCRIPTION*
COOLING
HEATING
TONS
$ X
MIL-BTU
$ X
A. 1/4-INCH SOLARBRONZE PLATE
657
$ 657
n.6
$ 198
B. 1-IMCH LHR SOLARBRONZE TWINDOW
641
641
11.3
193
C. MNCH SOLARBAN (2) TWINDOW
631
631
11.1
190
*ALL WITH INDOOR SHADING
430
MADISON BUILDING
TABLE III HEATING & COOLING SUMMARY (SX )
DESCRIPTION*
INSTALLED
G L A S^
COST
HEATING
&
COOLING
EQUIPMENT
COSTS
TOTAL
RELATIVE
DIFFERENCE
A. 1/4-INCH SOLARBRONZE PLATE
10.6
855
865.6
D. I-INLH LMK iOLAKoKUN^t TWINPOW
34.8
834
868.8
3.2
INCREASE
C. MNCH SOLARBAN (2) TWINDOW
30.6
820
850.6
15.0
SAVINGS
*ALL WITH INDOOR SHADING
431
MADISON BUILDING
TABLE IV COST ANALYSIS SUMMARY
INSTALLED
GLASS
COST
($)
HEATING &
COOLING
C WUI r Men I
COSTS
(S)
HEATING &
COOLING
U r C K A 1 1 nu
COSTS
($)
PRESENT
WORTH
($ per »q.ft.
rentable
floor area)
OWNING &
OPERATING
COSTS
($ per sq.ft.
rentable
floor area)
A. 1/4-INCH SOLARBRONZE PLATE
10,600
855,000
18,800
53.04
3.09
B. 1-INCH LHR SOLARBRONZE TWINDOW
34,800
834,000
18,300
53.36
3.11
C. 1-INCH SOLARBAN (2) TWINDOW
30,600
820,000
18,000
53.01
3.09
*ALL WITH INDOOR SHADING
432
COLUMBUS BUILDING
TABLE V GLASS ALTERNATIVES
DESCRIPTION*
U -
VALUE
SHADING
COEFFICIENT
INSTALLED
COST
i PER S Q . FT
A. 1/4-INCH SOLARBRONZE PLATE
B. 1-INCH SOLARBRONZE TWINDOW
C. 1-INCH SOLARBAN (2-3) TWINDOW
0.8
0.5
0.28
0.53
0.42
0.10
3.30
4.50
5.59
*ALL WITH INDOOR SHADING
433
COLUMBUS BUILDING
TABLE VI RESULTS
DESCRIPTION-
COOLING
HEATING
TONS
$ X
MIL-BTU
S X
A.
1/4-INCH SOLARBRONZE PLATE
3,114
3,114
23.21
371.4
B.
l-INCH SOLARBRONZE TWINDOW
2,763
2,763
17.41
278.6
C.
1-INCH SOLARBAN (2-3) TWINDOW
2,226
2,226
13.06
209.0
•ALL WITH INDOOR SHADING
434
COLUMBUS BUILDING
TABLE VII HEATING & COOLING SUMMARY ($ X )
DESCRIPTION*
INSTALLED
GLASS
COST
HEATING
&
EQUIPMENT
COSTS
TOTAL
RELATIVE
DIFFERENCE
A. 1/4-INCH SOLARBRONZE PLATE
$ 693
3,485
4,178
B. 1-INCH SOLARBRONZE TWINDOW
$ 945
3,041
3,986
192
SAVINGS
C. 1-INCH SOLARBAN (2-3) TWINDOW
$1,174
2,435
3,609
569
SAVINGS
*ALL WITH INDOOR SHADING
435
COLUMBUS BUILDING
TABLE VIII COST ANALYSIS SUMMARY
DESCRIPTION*
INSTALLED
GLASS
COST
($)
HEATING &
COOLING
EQUIPMENT
COSTS
($)
HEATING &
COOLING
OPERATING
COSTS
($)
PRESENT
WORTH
($ p»r »q.ft.
rentable
floor arte)
OWNING &
OPERATING
COSTS
($ per »q.ft.
rentable
floor area)
A.
1/4-INCH SOLARBRONZE PLATE
693,000
3,485,000
75,300
44.79
3.76
B.
1-INCH SOLARBRONZE TWINDOW
OAK (\(\r\
0|U4 1 ,uuu
A A A'i
i.l i
C.
1-INCH SOLARBAN (2-3) TWINDOW
1,174,000
2,435,000
60,800
43.64
3.66
•ALL WITH INDOOR SHADING
436
Comparative Computer Analysis
of the Thermal Cost Performance
of Building Enclosures
Willard A. Oberdick-"-
Smith, Hinchman & Grylls Associates, Inc.
Architects, Engineers and Planners
Detroit, Michigan
The computer programs on thermal-cost performance of build-
ing enclosure systems developed to be used in computer-aided
architectural design are described as to logic, data structure
and man machine interaction. The solar-climatic simulation
approach using normal Weather Bureau data for predicting the
thermal performance is compared to an hour by hour computer
analysis of selected examples. A mathematical model of the
total thermal energy system of a specific building is described
and used to evaluate the relative importance of the building
enclosure as well as compare computed data with that of metered
energy. This study proposes that specific modeling of specific
building thermal systems can be used to develop simulation
packages for use in computer aided design.
Key Words: Building enclosures, computer-aided design,
initial wall costs, man-machine interaction, owning
cost, present worth, building mechanical equipment,
thermal performance, solar- climatic simulation.
1. Introduction
The objective of the computer programs on thermal-cost performance is to provide
the architect with information in the design development or selection of components
for the building envelope, i.e., the walls and roofs. The programs can be used for a
variety of comparative studies involving thermal cost trade-offs. Initial and total
owning costs can be compared for specific building situations in specific locations.
The basic computer-aided design package was developed in and by
Smith, Hinchman & Grylls Associates, Inc., Architects, Engineers and Planners of
Detroit for use on an IBM. Subsequently, it was adapted to the IBM360/6 7 Time
Sharing System of the University of Michigan. This program package and video tape
instructions have been made available to the Department of Architecture for Educa-
tional purposes .
The objective of this paper is 1) to describe and evaluate the programs as a
computer-aided design method 2) describe and evaluate the use of Weather Bureau data
for such simulation and 3) to explore the concept of modeling of the total building
energy system as a means of checking simulation approaches used in computer-aided
design.
2. Design Development-Man and Machine
Many factors such as those related to the thermal, cost, luminous, sonic and visua
performance are considered by an Architect-Engineer in the design development of the
building envelope as part of the total building design. Of these, thermal performance
is particularly significant since it has implications from the standpoints of comfort,
direct and indirect costs and weatherability . The mechanical systems are dependent on
the nature of the envelope thermal loads. Therefore, not only are decisions by the
-'-Consultant; Professor of Architecture, University of Michigan, Ann Arbor, Michigan.
437
mechanical engineer required but effective design would indicate an optimizing approach
or at least consideration of interdependent trade-offs between building components and
mechanical equipment.
Since the computer program involves estimates of mechanical equipment costs, the
thermal loads must necessarily be compatible with the design practice of the mechanical
engineer, and as such he is logically involved in the entire process. Other facets of
the problem of program development involve the need for flexibility. Combinations of
advancing technology, changing building needs and variety of microclimates indicate a
maximum of flexibility in any data structure. However, tempering this requirement is
the need for simplicity of imput. These points together with the lack of computer
background of many who might logically use the system indicates the nature of the
challenge faced.
Experience to date indicates that the remote terminal is an ideal device for learn-
ing to use the programs and, in effect, to understand the system. Effort has been made
to improve the man-machine interaction with these programs using conversational imput,
default files for physical property and cost data along with an editing system. Once
the user has learned the system he may exercise the option of using either batch or
remote terminal as is appropriate in any particular case. Graphic display devices are
a logical next step when such are readily available. The user should in effect be a
team of a mechanical engineer and an architect or possess the insight of both for
effective use of the computer programs.
The problem of computational cost must also be considered. The general objective
is to obtain accurate information fast and at low cost. At one extreme is the complete
design and detail evaluation of complete buildings for comparative purposes. The
approach to simulation used in this system is intended to give specific effective
information at a minimum cost. As an example, with the University of Michigan system
the time used for the simulation-study is one fifth of that required for the detailed
hour by hour analysis noted subsequently in this paper. On an IBM, runs will
consist of from 5 to 10 minutes for several comparisons.
3. Data Structure
The heart of the problem from the user's standpoint is identification of the
specifics of the building and finding required information for use in the system.
The required data can be divided into five categories: wall type, mechanical systems,
wall conditions, solar-climatic conditions and economic data.
The approach used relative to wall types is that of identifying separate components
such as brick, block and glass, as shown in figure 2. Air spaces are identified as
separate components. Inside shading is included with the glass as a separate component.
A data assembly program TASSEM identified in figure 1, is used to select data from a
master file. The data includes cost information and physical properties. As an
example the user might type:
BRICK/EXTERI0R/4IN/
The computer would echo the data line with values in succession identified as: key
number, thickness, density, conductivity, specific heat, initial cost, maintenance cost
and maintenance interval.
14. 4. 130. 9. .18 1.73 .12 20. BRICK/EXTERI0R/4IN/
Transparent component are similar except the second, third, fourth items are, respec-
tively, total solar energy transmission, solar heat gain factor and the "U" value.
The type of mechanical system is identified in similar manner:
UNITARY /AIRCOND/HWBASE/
From the master file, figure 2, the following cost information is identified: key
number, cooling equipment costs, energy costs for cooling, heating equipment costs and
energy costs for heating all in dollars per BTU. The line would be echoed as:
81. .04 .024 . UNITARY/AIRCOND/HWBASE/
438
Wall conditions, figure 3, are defined with information on relative position, area,
percentage of glass, nature of ground reflecting plane and exterior shading as noted in
figure 4. In the latter case the actual position of the glass needs to be identified
in relation to the projecting surfaces. All of this data is sequenced and stored in a
Building Specifics File, figure 2. With the three groups of data the user in effect
identifies the building envelope and mechanical system.
The solar-climatic data is stored in a file and this is referenced in respect
to a particular location. The data is developed in accordance with the block diagram,
figure 5. The program identified as SOLCLIM in effect determines diurnal variations
from a year's data of drybulb temperatures, and cloud cover and with recorded normals
as input assembles the simulation data base of twelve prototypical days. The data for
the July day is shown in table 1. The first line from left to right consists of lati-
tude, elevation above sea level, outside surface film coefficient, solar radiation
constant for that month, days from equinox, season, average percent of sunshine. The
second line consists of projected diurnal temperature data for a day with average
temperature values at 3 hour intervals corresponding to those days with an average
cloud cover within the range of 31 to 69 percent. The average temperature is the normal
value for the month. The third line is similar except it consists of expected highs
with temperature pattern corresponding to 0 to 30 percent cloud cover. The maximum
is average of normal daily maxima and extreme high as recorded. The fourth line is
similar except that the cloud cover is 70 to 100 percent and lowest temperature is the
average of normal daily minima and recorded extreme low.
Table 1. Solar climatic normals for a prototypical day in July.
1
General
42
750
4
344
68
1
39
Time
1 A.M.
4 A.M.
7 A.M.
10 A.M.
1 P.M.
4 P.M.
7 P.M.
10 P.M.
2
Average
64
63
64
72
77
77
75
67
3
Highs
71
69
69
80
85
85
82
73
4
Lows
63
62
62
68
70
71
68
63
The data noted here and subsequent information on wet bulb temperatures were key-
punched directly from Local Climatological Data Summary sheets (1) . The same informa-
tion could be obtained from the Environmental Data Center in Asheville, N. C. and pro-
cessed for the immediate locale related to the observation station.
Information on long term costs are based on the concept of present worth of future
payments. Interest rate, years of anticipated use and the room temperature are entered
in running the simulation programs. Increasing attention is being placed on long term
or total owning costs. Although many more factors are involved in the total cost of
a building, the factors included in this system do permit effective comparative studies.
4. Program Logic
4.1 Basic Approach
Three concepts, thermal neutralization, solar climatic simulation and present worth
of future costs are fundamental to the logic of these programs. First, the concept that
mechanical equipment and energy will be considered to counteract any loss or gain from
the wall or roof; in effect, to obtain a thermally neutral surface. Involved are solar
and climatic effects on both transparent and opaque surfaces. Second; fundamental to
the prediction of the thermal performance is the simulation of the solar climatic
environment. The system included in these computer programs is intended to be micro-
oriented, that is, local temperatures, radiation intensities and ground reflections are
considered. Third, in order to compare future payments for maintenance or energy with
initial costs the concept of present worth of future payments is utilized. The equiva-
lent of a dollar invested with identified interest for future payments is assumed to be
comparable to the initial construction dollar.
*Note : Figures in brackets ( ) indicate literature referenced at the end of the paper.
439
In general, the approach has been to minimize the use of tables, in effect, to
use the methods that originally were used to generate the tabular values. This
distinction is a logical step from that of handbook engineering to computer-aided
design. Further, it has been necessary to improvise from basic research certain pro-
jected empirical relationships to fill program "logic blocks" where such have not been
advanced to the Engineering level. As an example, the interrelationship of cloud cover
to direct and indirect solar radiation and related transmission through glass required
programming expediency. In the latter case a second problem occurs when technical data
on product performance is not available on the detail required.
The primary problem is that of using logic that accounts for changing parameters
and is consistent in complexity throughout the program with intended use of the informa-
tion.
4.2 Solar Radiation and Heat Transfer
The basic program logic used for heat transfer and solar radiation was developed
in as part of research at the University of Michigan in reference to an evaluation
of polyurethane roof system (2). This was prior to publication of ASHRAE handbook
of Fundamentals (3) in which the first step was taken toward computer-aided design.
Direct solar radiation is computed for each of the hour-dates considered for
both a clear sky and a state of cloudiness as indicated. Factors considered are:
latitude, elevation above sea level, changing earth-sun distance, wall solar azimuth,
wall vertical position and cloudiness. For indirect radiation, cloudiness, intensity
of direct radiation (4) altitude of sun, wall position and irradiation (5) from the
ground are considered. The distinction is kept between direct and indirect radiation
in considering gain through transparent surfaces. The effect of direct radiation is
considered only in sunlit areas as determined by exterior shading patterns.
Heat transfer through opaque walls is based on an adaptation of the exact method
proposed by Mackey and Wright in 19 44 (6) for determining periodic heat flow through
walls and roofs. Decrement factors and lag angles for the first and second harmonics
are utilized. Factors considered are absorptivity of outer surface, outside film
coefficient, ambient air temperatures for a 24 hour period, direct and indirect solar
radiation, the density, specific heat and conductivity of each component and the
inside air temperature and inside surface film coefficient in respect to direction
of heat flow and position.
The program logic now incorporated for solar effects on the glass has been adapted
to use the coefficients (3) for transmittance and absorptance of glass. Total heat
transfer is based on prorated square foot of wall accounting for the proportions of
glass and opaque surfaces. Heat transfer from solar radiation and air to air tempera-
ture difference are considered for glass at the particular hour under consideration.
Transfer through opaque is considered at a prior lag angle hour using solar radiation
and ambient air temperatures of that hour.
In the research on polyurethane shell roofs (3) noted earlier limited field
observations were made as a check on the logic related to solar radiation and periodic
heat flow. The prototype structure consisted of seven, 14 foot hexagonal shells. A
temporary enclosure and heating was provided for the test period. Iron-constantan
thermocouples were installed in the roof and monitored manually at selected times over
a two month period and hourly over selected days. Results for a typical day are shown
in figure 6, Observations of cloud cover, wind velocity, air temperatures, surface
absorptivity were intended to parallel the computer logic. On the basis of this
correlation the idea of an hour by hour analysis was initially used in the develop-
ment of the concepts presently used in the solar climatic simulation.
4,3 Thermal Loads
In the simulation program heat transfer for expected high and low temperatures are
computed and stored separately in 12 by 8 arrays. As each surface in an identified zone
is computed it is added to respective array. Peak heat gain and loss are determined by
searching the accumulative values in the arrays. These are based on a clear sky and
should, in effect, be the basis of design. Equipment costs are based on these values.
440
In addition, heat transfer under specified cloudiness with both highs and average
temperatures are accumulated for each wall at the 96 prototypical hours for annual
gross loads per se in these programs.
4.4 Costs
Initial costs of wall are the accumulative prorated sum of the costs of identified
components. Initial cost of mechanical equipment for thermal neutralization is the
product of peak loss and gain and the respective estimates of costs per BTU capacity
for the particular system.
Energy costs are based on annual costs for energy for heating and cooling and are
the products of accumulative loads and respective energy costs per BTU. The present
worth (7) of future annual payments is used for the comparative figures. As an example
for twenty equal payments the present worth equal 11,4 7 times the annual value.
Maintenance costs are based on the accumulated prorated sum of the present worth
of future payments for maintenance on each of identified components.
Total owning costs then are the sums of initial, energy and maintenance costs.
5. Simulation-Thermal Cost Performance
The first example used to illustrate the application of the programs and as a test
case for comparing the simulation programs with that of the detailed analytical program
is the Cooley Building located on the North Campus, University of Michigan. The two
story rectilinear building, figure 7 was built twenty years ago without air condition-
ing. The thermal performance of the building was such that an exterior shading screen
was subsequently installed on the south glass wall. The summary of the output, table 2
indicates the trade-off for changes in the south wall with and without air conditioning
It should be noted that the south wall accounts for only one-quarter of the total
envelope area and as such the substantial changes in heat gain from 124 to 5 8 BTUS
per square foot for the south wall without and with the screen, is reflected in reduced
values when considering the entire building surface. The total owning cost for air con
ditioning with the exterior screening is $7.45 per sq. ft. of envelope as compared to
item 4 involving an alternate of Venetian blinds.
Table 2. Thermal Cost Comparison for the Cooley Building, North Campus,
University of Michigan, Ann Arbor, Michigan
No.
Type
South
Wall
Mech .
Sys .
Initial
Wall Cost
Mech .
Equip.
Cost
Mainte-
nance
Cost
Energy
Cost
Total
Cost
Gain/Loss
BTU/Sq.Ft
1
SN
Basic
Heating
2.67
0.75
. 39
1.28
5.08
28.5/-37.
3
Only
2
SN
+Outside
Heating
2.90
0. 75
. 39
1.27
5. 31
16.9/-37.
3
screen
Only
3
SN
Basic
Air
2.67
3.60
. 39
1.96
8.61
28.5/ 37.
3
Cond.
4
SN
+Venetian
Air
2.78
2.44
0.42
1. 72
7.63
19.9/-35.
6
Blinds
Cond.
5
S69
+Venetian
Air
2.78
2.60
0.42
1.69
7. 50
19.2/ 34.
1
Blinds
Cond.
6
A69
Venetian
Air
2.78
2.99
0.42
1. 83
8.03
22. 2/- 38.
2
Blinds
Cond.
SM
- Simulation Normals
; S69 - Simulation
Data Equivalent for
A69
- Detailed
"Year-Hour" Analysis
All
values are
for a prorated average square foot
for the five
surfaces
Basic south wall consists of brick and cinder block with 71% clear glass.
441
Items 4, 5 and 6 in table 5 are for the same building condition, in effect, the
same Building Specific File is used in each. The simulation data for Ann Arbor is used
in item 4 along with simulation program WTHERM, figure 8. Item 5 involves values
in a simulation form, figure 5. Item 6 involves results from program WTHERMA, figure 9,
a detailed analysis for . The results are not exact but reasonably close for com-
parative purposes.
The second example the Institute of Science and Technology on North Campus,
University of Michigan, involves a unique shadow box shading device. Results from
the simulation study indicate an initial cost of glass of $3.10 and mechanical equip-
ment cost of $10.20 and present worth of energy costs of $4.30 per sq. ft. of glass.
The minimum shadow during period of gain for the west wall is 22 percent, figure 10.
The cost trade-off for the shading device for the west wall is $2.57 per sq. ft.
of glass. This was obtained by another run omitting the exterior shading.
6. Modeling of Building Thermal Energy Systems
It is proposed that the accuracy of the simulation approach can be evaluated by
modeling the total thermal energy system for a building and comparing the prediction
of energy consumption with that metered. The Undergraduate Library, figure 11, at the
University of Michigan was used as a case study. The building has nearly a constant
year around occupancy, further, monthly turnstile figures, recorded electrical energy
consumption for the building and monthly recordings of condensate were available. The
computer program system used for this building is blocked out in figure 9. Program
WTHERMA referred to in the previous section was used to obtain the 3-hour interval
heat loss or gain of the total building envelope. Although the building appears simple
in form, 12 separate surfaces were identified to cover combinations of brick and glass,
stone and glass and porcelain steel panels and glass combinations. The maximum heat
loss for the 63,600 sq. ft. of envelope is only 16.1 BTUS per sq. ft. and the gain of
7.1 BTUS, indicating a minimum influence of the envelope.
The program ULGUM in effect, is a model of the energy aspects of the air condition-
ing system. The system is a central system consisting of 6 supply fans with a total
capacity of 163,000 C.F.M., a reheat system for zone control, a hot water convector
system and a chilled water system using steam in Lithium Bromide absorption machine with
a cooling tower. Cooling equipment was turned on April 28 and off on November 2 in .
On the same dates basic control of outside and return air damper were changed. Involved
in this program are predictions of room temperatures and relative humidity of room air.
For each of the three hour periods in the year, room conditions, percentage of
outside air, as well as required wall heat, reheat and cooling are determined. Lighting
and number of occupants are predicted for that specific hour. A summary for each month
is included in table 3. Several runs with different cold deck temperatures and slight-
room temperature variation resulted in sufficient difference in total energy to indicate
that the preciseness of system control is essential for closer correlation.
Table 3. Thermal Cost Comparisons for the Operation of the Undergraduate
Library, University of Michigan
Month
Enve lope
Gain
-Energy
Loss
Occupancy
Gain-Energy
Reheat
Energy
Cooling
Energy
Total
Energy
Metered
Energy
Total
Cost $
Jan .
0
494. 5
1,113.9
1,471. 4
0
1,963.9
1,600.0
3,224.
Feb.
0
395 .9
1,180.9
1,338.6
0
1,734.4
1,250.0
2,844.
Mar.
0.4
362 .2
1,053.9
1, 758.9
0
2,121.1
1,100.0
3,478.
Apr.
4.2
180 . 8
1,133.0
1,139 .9
0
1,319,7
1,821.0
2,164.
May
18. 7
103. 6
712 .6
1,632.5
577. 3
2 , 313. 3
2 ,120 .0
3,793.
June
36. 8
53.5
832.1
1,251,541
2,574.6
3,878.6
2,011.0
6 ,360 .
July
72.6
7.1
705.0
1,340 ,173
5 ,200 .6
6,547.9
5 ,103. 0
10 ,737.
Aug .
83. 2
7.1
731. 9
1,222.5
4,523.0
5 , 752. 6
5,747.0
9,433.
Sept.
16 .6
66.1
873.6
1, 269 .0
2,293.3
3,628.4
6,246.0
5,949.
Oct.
0.8
197. 1
1,016 . 1
2,563.5
614.9
3,375.6
4,449.0
5,535.
Nov.
0.1
330 .3
1,046.5
1,642.6
0
1,972.9
1,579.0
3,235.
Dec.
0
463 .1
1,083. 9
1,661.4
0
2,124.5
2,266.0
3,484.
Total
233 . 3
2,661.1
11,483. 3
18,291. 1
15 ,783. 6
36 ,734. 8
35,292.0
60 ,244.
Note: Total energy equals the sum of envelope loss, reheat and cooling.
All energy values are noted in MIL BTUS
Costs are based on a projected steam cost of $1.65 per lb.
442
The relative influence on costs of the envelope are shown in table 4, for the
Library and a hypothetical library occupancy for the Cooley Building, Case II. The
latter having a larger wall to floor area ratio and a thermally responsive glass south
wall. The system cost figures used in this case have been adjusted to be consistent
with those used for equipment and energy in the Library, Case I.
Table 4. Comparison of Building Envelope and Mechanical Equipment Costs in Buildings
Case II.
Case I. Cooley Bldg.
Undergraduate Library Hypothetical Library
Floor Area
Envelope Surface Area
Envelope Cost
Equipment Costs for Envelope Neutralization
Equipment Cost for Total Building
Energy Cost for Envelope Neutralization -
Present Worth 20 Years
Energy Cost for Total Building -
Present Worth 20 Years
136,680 sq.
6 3,363 sq .
$ 1.46
$ 1.64
$10.08
ft.
ft.
0.40
6.19
26,072 sq.
28,644 sq.
$ 3.06
$ 3.77
$10.99
ft.
ft.
2. 30
8.23
Cost Values are in $ per sq. ft. of floor area.
7. Conclusions
The simulation approach for identifying wall performance is an effective computer-
aided design tool. Expansion of the concept to the total system is required to give
the design team an accurate cost performance picture of the building.
The use of normals from accumulative Weather Bureau Data for this simulation has
been compared to that obtained from a detailed year-hour analysis. The same procedure
should be used for a larger number of years to provide a statistical base for correla-
tion. Detailed checking of program logic or blocks can be accomplished by isolating
the parameters for specific correlation with field measurement of temperatures.
The results of the total thermal energy study are inconclusive but do indicate
the potential not only as a check for this simulation approach but as a direct benefit
to the owner in optimizing the operation of his building. Further, idiosyncrasies of
the building operation, such as down time for cooling equipment; and accuracy of
metering must be taken into account.
8. References
[1] Local Climatological Data, Asheville,
North Carolina, U. S. Department of
Commerce, Data Sheets - Detroit,
Michigan, .
[2] Oberdick, W. A., "Design and Evalua-
tion of a PolyuretHahe Foam Shell Roof
System, " Ann Arbor, Michigan, ARL
Report, 196 6.
[3] ASHRAE Handbook of Fundamentals, New
York City, Am. Soc. Heat., Refr. , and
Air-Cond. Engrs. Inc. pp. 475-479, .
[4] Robinson, N., Solar Radiation, Nether-
lands, Elsevier Publishing Co., .
[5] Threlkeld, J. L., Thermal Environ-
mental Engineering, pp. 356, 360,
(Prentice Hall, ) .
[6] Mackey, C. 0., Wright, L. T. , Jr.,
"Periodic Heat Flow-Homogeneous
Walls or Roofs, " Trans. Am. Soc.
Heating and Vent. Engrs., Vol. 50
(No. ) , pp. 293-312 , .
[7] Grim, C. T. , Gross, J. G. Ultimate
Cost of Building Walls. Washington,
D.C. Department of Engineering and
Technology, Structural Clay Products
Institute, .
443
KEY WORDS
SELECTED INFO-
INPUT
PROMPTING
ECHOED DATA
OUTPUT
WALL CONDITIONS
POSITION, AREAS
GROUND PLANE
EXTERIOR SHADING
T ASSEM
DATA ASSEMBLY
MECH- SYSTEMS
WALL TYPES
WALL CONDITIONS
MODES
TTY- CONVERSATIONAL
BATCH-NUMERIC
B UILOI NG SPECIFICS
INTERMEDIATE FILE
MECHANICAL
MASTER FILE
SYSTEM COSTS
SELECTION a EDITING
SELECTI ON a EDITING
MATERIALS
MASTER FILE
PROPERTIES a COSTS
Figure 1
Block diagram - data assembly of building specifics
FACE BRICK
• • • 1 •
f 1 • •
a ■ • • ■
Wa
• • • •
' ■ • • •
m
■ ■ ■ ■
' • ■ ■
8
CINDER BLOCK
CLEAR GLASS
Figure 2 Wall types - Cooley Building South Wall
444
Figure 4 Exterior shading - data re^jresentation .
445
WEATHER BUREAU DATA
SUMMARY VALUES
NORMALS a EXTREMES
SIMULATION DATA
NORMAL VALUES
12- PROTOTYPICAL DAYS
S 0 LCLIM
CONSTRUCTION OF
SIMULATION SOLAR
CLIMATIC FILES
DIURNAL VARIATIONS
HIGHS -AVERAOES-LOWS
WEATHER BUREAU DATA
DRY BULB TEMPERATURE
CLOUD COVER
I YEAR - 3 HOUR INTERVALS
SOLAR CLIMATIC
SPECIFIC YEAR
12 - PROTOTYPICAL DAYS
Figure 5
Block diagram - solar climatic data
REFERENCE PLAN
SECTION (A)
£ 60
" 50
o/
//■
-^■■■■tr 7
-h
O G
o e
100% SUNSHINE
H-7m
N
OUTSIDE AIR
0 % SUNSHINE
■■(CO
G
MPUTED)
• 7m
6 AM 8 10 12 NOON 2 PM 4
EASTERN STANDARD TIME
NOTES CURVES ARE FOR RECORDED VALUES EXCEPT AS NOTED
DATE MAY 2, I9«6
AVERAOE WIND VELOCITY = 7.9 M.RH.
Figure 6 Correlation studies of diurnal variation of temperatures in a
polyurethane shell roof.
446
CONTROL DATA
TEMPERATURE, YEARS
INTEREST RATE
INPUT
DETAIL THERMAL CONDITION
ELECTIVE SHADIN6
PATTERNS OUTPUT
SUMMARY OF COSTS
AND THERMAL CONDITIONS
OUTPUT
WTH ER M
ANALYSIS OF
ENVELOPE-
HEAT LOSS a GAIN
INITIAL COSTS
MAINTENANCE COSTS
ENERGY COSTS
BUILDING SPECIFICS
INTERMEDIATE FILE
SIMULATION DATA
12 PROTOTYPICAL DAYS
Figure 8 Block diagram of the thermal cost performance simulation program
CONTROL DATA
TEMPERATURE, YEARS
INTEREST RATE
LATITUDE, ELEVATION
INPUT
ENVELOPE
OWNING COSTS
THERMAL
LOADS
OUTPUT
ELECTRICAL ENERGY
OCCUPANTS
SYSTEM FACTORS
INPUT
CUMULATIVE ENERGY COSTS
BY HOUR, MONTH, YEAR
OUTPUT
WTH ER MA
ANALYSIS OF
ENVELOPE
- 3 HR INTERVALS
HEAT LOST a GAIN
INITIAL COSTS
MAINTENANCE COSTS
ENERGY COSTS
HEAT TRANSFER-3HR-
U G L U M
ANALYSIS OF
MECHANICAL SYSTEMS
ENVELOPE
LIGHTING
OCCUPANTS
VENTILATION
BUILDING SPECIFICS
INTERMEDIATE FILE
WEATHER BUREAU DATA
DRY BULB TEMPERATURES
CLOUD COVER
I YEAR -3 HOUR INTERVALS
WEATHER BUREAU DATA
WET BULB TEMPERATURES
I YEAR -3 HOUR INTERVALS
Figure 9 Block diagram of the computer programs for modeling of the thermal
energy system in buildings.
448
Figure 10 Shadow box window enclosure and line printer output of shadow pattern
Institute of Science and Technology, North Campus, University of Michigan
449
450
A Numerical Method for Computing
the Non-Linear, Time Dependent,
Buoyant Circulation of Air in Rooms
Jacob E. Fromm
IBM Research Laboratory
San Jose, California
A method is described which solves the dynamic equations for air circulation
at Grashof numbers that are in the range of environmental temperatures of rooms.
Previous computation techniques were limited to G ~10^, but environmental condi-
tions require G ~10-'-^. The higher Grashof numbers are attained by improved non-
linear approximation methods. Fourth order difference equations are discussed rel-
ative to linear stability properties which determine the fidelity of the convec-
tive process in the finite net of points. Non-linear instability of time-splitting
methods is described and the means of overcoming this type of instability are given.
Key Words: Heat transfer, finite difference, computation, convective
approximations, air circulation, time dependent solution.
1. Introduction
In the past decade numerous advances have been made in the use of numerical means to solve
coupled non-linear partial differential equations. The methods for obtaining solutions fall roughly
into two categories: i. Expansion methods which make use of orthogonal polynomials; 2.
Finite difference methods. The former of these was used by Poots^ and the latter by Wilkes"^ for the
particular problem of interest here. The success of the two methods of solution relative to the work
of the cited authors was about the same. Comparable solutions were obtained for the problems of buoy-
ant fluid flow in a two dimensional enclosure with vertical walls at a fixed temperature difference
and horizontal walls either insulated or with a fixed temperature which varied linearly between the up-
right walls. These successes were important ones and led to the hope that the methods could readily be
extended beyond the range of parameters of those studied into the practical problems of everyday engi-
neering experience, in particular to the study of air circulation at environmental room temperatures or
under fire conditions.
Both the methods indicated above do possess the potential of providing solutions to such problems.
Currently, the greatest emphasis is on finite difference methods because they may be applied in a
straightforward manner if sufficiently accurate algorithms are known. Unfortunately, such algorithms
have been slow in realization. Here we have utilized higher order approximations that depend upon flow
direction. This is essential in order that detail may be maintained without introduction of noise com-
ponents which are of numerical origin. The nature of the flow in the rectangular enclosure is such
that the common weaknesses of non-linear difference approximations are very pronounced. Thus while the
geometrical situation is fairly simple it provides a crucial test of the methods.
Our primary objectives here are to outline the numerical methods and to give details of the al-
gorithms that are required. The general procedure of finite difference computation using the vorticity
and streamf unction as field variables is fairly well established^'**'^. Also, the evolution of thought
on requirements relative to reduction of phase error, which is the primary cause of computational noise,
has been documented^ ' ^ . The additional modifications of the basic algorithms that are pertinent for
the success of high Grashof number calculations are emphasized here.
As a result of these efforts toward minimizing numerical noise and numerical damping, the two-dimen-
sional computation can reasonably be carried out up to Grashof numbers of 10^^. At these high values
there are uncertainties about the magnitude of viscosity and heat transfer coefficients relative to
truncation errors. Further, very small time increments are required for computation. Hence, the
limiting calculation of infinite Grashof number would not be a reasonable one.
Because turbulence is surely a factor in the real world, the present calculations using molecular
451
coefficients should be regarded as idealizations. This does not mean that they are of little value.
On the contrary, we can analyze the flow behavior, explaining the flow features that occur and why
they occur. Further, gross properties of the flows can be given within the framework of the idealiza-
tion. With this information it should be possible, with the help of experiments, to determine where
discrepancies occur between observation and computation. Information so obtained is pertinent to
modeling efforts where turbulent diffusion and heat transport must be parameterized.
2. Governing Equations and Problem Description
The conservation equations to be solved in a two dimensional rectangular region are:
Mass: ^ + = q , (1)
Momentum: tt— +u — + v— = — + vVu, (2)
dt dx 3y p 3x
o
3v , 3v , 3v 1 3P l'^ '^o^
+ u — + V
3t 3x 3y p 3y ^ T
o \ o J
+ vv^v , (3)
3T ^ 3T , 3T „2„
Energy: _ + u — + v — = kv T . (4)
Here u and v are velocity components in the x and y directions respectively. The thermo-
dynamic variables p, P, and T are the density, pressure and temperature respectively. The sub.-
script o indicates constant reference values to be defined, v, k, and g are the kinematic vis-
cosity, thermometric conductivity and gravitational constant respectively.
Numerical computation is carried out using the vorticity and streamfunction. We define
to = 7— - 7— (5)
3y 3x ^
and
" = 97 ' " = - •
Thus (1) is satisfied identically by (6), (5) becomes
2 2
— 5" + — T = - 10 , (7)
3x 3y
and P can be eliminated from (2) and (3) yielding the vorticity equation
w'-u . (8)
3(1) , 3uu , 3vu 3^ + .."Z
3t 3x 3y T
o
Our system of computation equations are then (7), (8), (4) and the definitions (6).
We take x as the horizontal coordinate and impose the boundary conditions for a square enclosure
u=v=o, T=T^ at x=o for o <_ y <_ d
u=v=o, T=T at x=d for o £ y £ d
at y=0 ,d for o _^ x
T=T,-x(T,-T )/d
1 1 o
at y=o,d for o < x < d
(9)
452
It is found more convenient to deal numerically in terms of the dimensional variables because of
physical interpretation and number sizes encountered in numerical solution. Following Foots we use
the nomenclature
a = v/k
as the Prandtl number and
A = a G = (T -T ) gd^/T kv
i o o
for the Rayleigh and Grashof numbers respectively.
While numerous gross properties could be evaluated to lend understanding to the flows, we here consi-
der the dimensionless heat transfer for comparison with results by Foots and Wilkes. Heat transmission
through the cold vertical boundary is not the total heat transmission but is the value given by Foots.
Numerically, one must also include the convection flux because the discrete description requires it.
For the square region considered we define the Nusselt number
N = ^ .
1 o
The total heat transmission can be evaluated only by having the end points of the integration corres-
pond to x=d/2 and y=o,d. Nevertheless, for comparison purposes we also measure the transmission at
x=o with integration limits y=o,d.
3. The Numerical Approximations
We now describe the non-linear approximation method that was required for the success of the
given calculations. For completeness we shall outline the numerical procedure, giving the numerical
approximations but postponing the convective flux methods for later discussion.
For small values of A or G it may be advisable to initialize calculation with no flow and an
initially prescribed linear horizontal temperature variation inside the fluid region. If A is small,
steady state results are of primary interest and computation time may be preserved by relay type calcu-
lations, always using steady state results from lower values of A to proceed to higher values. How-
ever, beyond A=10^ the solutions are unsteady, in fact A=10^, 0=0.1 gives an oscillating solution.
While it is always useful to begin with an approximate solution to the expected solution at late time,
it is more reasonable to initialize calculation at high values of A with internal temperatures spec-
ified to be everywhere the mean of the given wall temperatures. If the initial interior temperature
is specified to be that of the low temperature wall, much computation would be required to approach
true late time conditions. In all cases reported here, we initialized the temperature field to have
the mean wall temperature value. The streamf unction and vorticity were perscribed to be everywhere
zero initially.
With all field values given at the time t=o we proceed by updating the temperature field toward
ultimate prescription of field values T, . = T(iAx, j Ay ,nAt) for n=l. Through convective flux com-
putation we first obtain everywhere
i,j i,j Ax [ i'-l/2,J 1+1/2, jj Ay 1^^1,3-1/2 *i,j+l/2j
(10)
where F is the flux at half cell distances from the point (i.jj. Using everywhere the tantative values
(except for fixed values at the boundaries) we add the conduction contribution to complete the update
j of T. Thus
T. . = T. . + ( T.^, . - 2T. . + T. , .
+ f T. - 2T . . + T. . , 1 . (11)
453
The use of tentative updated values in the conduction calculation provides for less restrictive
conditional stability of this explicit difference equation. This has been suggested in the work
ofMarchuk^ and has been observed empirically in the present calculations. Through this procedure the
stability condition
KAt/ min[(Ax)2,(Ay)^]
i.J i>J (^2^)2 [ 1+1, J i,j 1-1, jj + — ^ 1,1+1 1,1 1,3-lj. (14)
Finally the buoyancy contribution gives the complete update of to thusT
u! . = to* . + (t'^_^^ • - t"!" , .] (15)
1,3 i,j 2T^Ax V 1+1,3 1-1,1 j
Note that the values obtained in (11) are necessary in (15). If in (15) the old time values were used
instability would result.
With T and to both obtained for new times we next consider the streamf unction field. Simultaneous
solution of all net points is required to satisfy
1 11 1 11
(Ax) Ay"^
Because of the simplicity of the boundary conditions on ij; a direct method may readily provide solution.
We have here made use of a program developed by Buneman^. Buneman's method involves cyclic matrix re-
duction in two directions. It is applicable to an enclosed rectangular region with zero value speci-
fied for ijj at the boundaries. The program is fast, accurate to computer round off, and compact.
It is estimated that an iterative method would have taken more than ten times as much computation for
equal accuracy.
The final step in computation of the field variables, to have a complete solution at the advanced
time step, is to apply no-slip conditions at the walls, i.e., obtain boundary vorticity values. The
approximations here used are
1 /'I 1 '1 2
1 r 1 1 ^ , 2
^i,i = ' - Vi,jJ/'^^
1 r 1 ,1 ^ , 2
^,0 = -2 [^i,i- \,o] i^y
1 1 1^,2
where o refers to left or lower boundary and I and J refer to right and upper boundaries respec-
tively. The equations (17) may readily be derived from (16). Comer values of to are always zero
as implied by successive use of appropriate parts of (17).
454
Stability of the explicit form of solution is tested at all time steps and provision is made to
double or halve the time step. If the larger of uAt/Ax and vAt/Ay Is less than 0.4 the time step
is doubled. If the larger of uAt/A x and v At/Ay is greater than 1.0 the time step is cut in half.
Applying these conditions along with (12) maintains stability throughout the forward marching problem.
While an initial estimate of At is not required by this procedure some early time rapid adjustment of
At does occur for large A. In these cases a maximum early time At should be used for the first se-
veral time steps because a very large At is implied by the stability conditions. Eq . (15) is over-
stable and no test is necessary for this part of the procedure.
With a view of the overall procedure we now give further consideration to F of Eq. (10) or H of
Eq. (13). Both F and H are, in computation, handled by the same program. Prior experience led to
fourth order one dimensional approximations for F on the assumption that "time splitting" methods would
be used to provide isotropic behavior relative to the finite lattice. "Time splitting" is a process
which involves computation of tentative values through the addition of horizontal flux contributions
followed by additions of vertical flux contributions. Here the latter computation makes use of the ten-
tative values derived from the horizontal additions. In a linear sense "time splitting" results in the
inclusion of diagonal values of the field variable such that truly two dimensional flow is treated. It
is an efficient way to obtain isotropic behavior since without "time splitting" or some equivalent pro-
cedure one may, in the extreme case, experience instability in the flow direction simultaneous to numer-
ical diffusion transverse to the flow direction. Often these two effects can hold the numerical com-
putation in check but the results may be badly in error since distortion occurs here even if the flow
is uniform but not along the coordinate axes. In two-dimensions then we must in some sense bring in
mesh values of the field variables that are diagonally distributed relative to the coordinate directions
at (i,j).
Unfortunately, while "time splitting" is an efficient procedure to use it has been found that
a new type of instability can occur. This instability is slow and occurs only in non-linear cases. In
the given problem a vortex originating from buoyant effects may grow in intensity in a non-physical man-
ner. This difficulty is not very different from that of using non-conservative difference methods. It
is perhaps less severe. Its degree of severity depends upon the non-linearity of the problem and the am-
plitude characteristics of the approximation. The difficulty has its origin in an inconsistency that
occurs in the velocity values that are effectively present in the implied cross differences. Since the
cross derivatives are implied through "time splitting", this shortcoming goes unnoticed until the slow
growing instability occurs.
Here the difficulty is circumvented by explicitly programming cross derivatives as required to pro-
vide the linear equivalent of "time splitting" procedures. By so doing the linear stability conditions
are maintained and the inconsistencies in velocity values are avoided. If one expands the "time split-
ting" equations into a single step the cross differences will appear. Using these terms as a guide,
final layout of conservative expressions are developed from a Taylor's series expansion*. Consider
T"+1 = T'^+At ^'^^ ■ '^'^^
3t J 2 I ^ 2
Because we are numerically separating convection and conduction we take
il = _ IhI _ Ai^
at 3x 9y
If we make use of (19) in (18) and drop velocity time derivatives we obtain
(18)
(19)
3^T _ 9 12 3^T 3T I, 3 f 3T _|_ ^ j ^^q)
, 2 - 3x r + 3y !■ 3y I - 2 ■ - 2
3t ^ 3x ^ J ^ y 3y
Here the (uv) terms are the first cross terms that must be explicitly programmed rather than implied
as in "time splitting". The (uv) term has two parts, one part is regarded as a skew flow correction
to the flux in the x direction, the other part as a skew flow correction to the flux in the y di-
rection. With similar expansion of (18) to eighth order all cross differences for fourth order approxi-
mation may be developed. Proper combination of these terms can lead to simple expressions and reason-
ably fast computation. The fourth order forms are giveft in the Appendix.
One further consideration in the convective approximation is phase distortion. It is particularly
This technique was first employed by S. K. Jordan in his Doctoral thesis "Numerical Solutions for the
Time-Dependent, Viscous, Incompressible Flow Past a Circle," Department of Aeronautics and Astronautics,
Stanford University, .
455
pertinent to the problem at hand since the usual difference methods would quickly lead to meaningless
results for A>10^. It is essential to success of such calculations to have leading phase errors and
these should be small. Upstream approximations may be used to achieve this and if necessary several
different approximations may be linked through different magnetudes of a = uAt/Ax. Here we have used a
combined fourth order upstream and central approximation (flow direction must here also be tested) for
a >_ 0.5. For 0.90 ^ a _< 0.5 the fourth order upstream approximation alone is used. If a < 0.09 a
second order upstream approximation is used. Central approximations are used only for flow away from
solid boundaries if data points for upstream calculation are not available. In these latter instances
lagging phase errors do not lead to noise. The use of second order upstream approximations for a < 0.09
has to do with an anomoly in fourth order characteristics that is not present in second order. The
above procedure is not the only one that may be used. In the given case it was the most expedient on the
basis of available data on phase properties of the methods. The choice made also included consideration
of amplitude properties to limit numerical damping.
4. Flow Behavior
At the time of this writing we have computed several cases to give an overall view of variation of
flows with different Rayleigh number and Prandtl number. Computations have been made for A = 10**
through A = 10-^^ at intervals of a factor of 10 and with a=1.0 For even powers of A, runs were
also made for a = 10.0 and a = 0.1. From these computations the flows can be classed roughly
into three groups. 1. Steady state flows (G < lO'') ; 2. Transition flows, unsteady and highly vari-
able in behavior (10^ < G < 10^) ; and 3. Single circulation, high Grashof number flows (109 < G < 10l3).
The steady state flows are also single circulation flows characterized by the presence of a
vertical temperature gradient in the central region of the enclosure but little horizontal temperature
gradient. The temperature gradients increase strongly near the walls. This type of behavior is illus-
trated in the steady solution of A = 10^, a = 1.0 of Fig. 1.
In the transition flows the variable behavior includes sinusoidal behavior at the low values of G.
Mid-transition flows deviate from sinusoidal to include random occurances of buoyant plumes along the
horizontal boundaries. In the upper transition flows randomness is increased and boundary layer en-
trainment leads to counter circulations mixed with buoyant circulations. Figure 2 is an example of
upper transition range flow.
Members of the last group are classed together because visually they exhibit little difference in be-
havior. A single circulation (in the square region) is the main feature and is common to the whole
group. The interior fluid is essentially isothermal at the mean temperature and vorticity is almost
completely absent there. One can describe these flows as having an inner core of ideal fluid flow and
a highly variable boundary layer behavior. The thermal and velocity boundary layers are thin but comer
regions are involved in the flow related to these layers. In Fig. 3 we include an example from this group.
Returning now to Fig. 1 we consider this group in more detail. In Fig. lA the streamlines of the
flow are given. The highest speeds, as expected, are of flow near the vertical boundaries while the flow
near the center is slow. The separated centers of circulation are in the same direction of rotation.
They occur because of two regions of buoyant vorticity associated with the heated and cooled vertical
walls. They are separated by a reverse flow tendency which has its origin in a slight reversal in the
horizontal temperature gradient. In Fig. IB one notes that the highest values of vorticity occur at the
boundaries. The sign is opposite to the two buoyant vorticity extremals occuring near the vertical walls.
This is the boundary layer vorticity which follows from our no-slip condition. The central extremal of
vorticity is also of opposite sign to the main buoyant contributions. It also has its origin in buoyancy
but here in reverse to the main circulation. This reversed vorticity contributes to the attainment of
steady flow in this range, along with the dissipation or frictional restraining forces. The latter mec-
hanism is of coarse strongest at the boundaries. In the isotherms of Fig. IC one clearly sees the slight
reversal in horizontal temperature gradient at the center (the slant of the isotherms is downward to the
right) . Increased heat transfer relative to a non-fluid material is obvious from Fig. IC in that the
flow leads to high gradients in temperature at the vertical walls. Near the walls conduction is in-
hanced by the high gradients and in turn the flow in the center leads to exchange of warm and cold fluid
through the convective process.
The results of Fig. 1 are not new,, similar results have been obtained by Wilkes and Foots. To es-
tablish a point of departure from this earlier work we have compared a calculation of A = 10**, a = .73
with the results by Foots. The results are the same in all essentials in the visual sense of the solu-
tion. To further compare results we have numerically obtained the Fourier coefficients of our computed
result for the disturbance temperature field (the linear gradient with T-|^-T =1.0 must be added to ob-
tain the equivalent of Fig. IC) . In Table I we compare the numerical coefficients with coefficients
given by Foots. Differences in the results cannot be construed as error in the numerical results because
the analytic solution is also approximate. The differences in the second group of coefficients of Table
I is puzzling and may be an error by Foots in recording the numbers. Consistencies for even smaller co-
efficients is good. Measured heat transfer at the cold wall as obtained by Foots is N = 1.706. We ob-
tained N = 1.75 3 numerically.
456
Table I. Fourier coefficients of disturbance temperature distribution for A = 10 , a = .73
Term (kx.ky)
Poot's
Finite
Difference
1,2
2,1
-0.
-0.
-0.
-0.
1,4
2,3
3,2
4,1
0.
0.006 3
-0.
-0.
-0.
-0.
0.
-0.
1,6
2,5
3,4
4,3
5,2
6,1
0.
0.
-0.
0.
0.
-0.
0.
-0.
-0.
0.
0.
-0.
1,8
2,7
3,6
4,5
5,4
6,3
7,2
8,1
0.
0.
0.
0.
-0.
0.
0.
-0.
0.
0.
-0.
0.
-0.
0.
0.
-0.
1,10
2,9
3,8
4,7
5,6
6,5
7,4
8,3
9,2
10,1
0.
0.
0.
0.
-0.
0.
0.
0.
0.
-0.
0.
0.
0.
0.
-0.
0.
-0.
0.
-0.
-0.
I, 12
2,11
II, 2
12,1
0.
0.
0.
-0.
Proceeding to Fig. 2 we include results for A = 10^, a = 1. In this range we have passed consid-
erably beyond the point where solution was previously possible. The results portrayed in Fig. 2 are a
sinf.le still portrait of a rapidly varying flow. Standing alone these photos do not yield much under-
standing of detailed behavior, nor do we necessarily need detail of the origin of every small vortex.
Animations of these solutions have proved to be valuable. With motion picture films of various represen-
tations new insights into the behavior become possible. The most important mechanisms beyond those evi-
dent in Fig. 1 is that boundary layer separation occurs and counter circulations to the main buoyant
tendency can arise. IVhen these do arise they may influence the temperature field sufficiently to be
enhanced by buoyant effects. Reinforcement of counter circulations by buoyant forces is present in the
case of Fig. 2. The instabilities that occur because of these successive effects are probably only
part of the influences that prevent the emergence of a steady state. In the transition range, steady
state is probably impossible although resonant effects might possibly be achieved through a highly
critical choice of rectangular dimensions of the enclosure.
In Fig. 2A the separation streamline is given and counter circulations may be identified by tracing
this streamline. Those circulations falling in regions toward the boundaries (exterior to the separation
streamline are counter circulations). The remaining significant centers of rotation are in the direction
of the basic buoyant tendency. In the vorticity plots of Fig. 2B we note that the buoyant contribution
from the vertical walls is confined to a very narrow vertical strip and this strip may be broken up into
small concentrations. These concentrations move upward along the heated wall much like air bubbles in
water and give a wave character to the streamlines. Dominant characteristics in this range of A, even
457
in the presence of the rapid time variation, are the strong circulations in the upper left and lower
right corners. These circulations are inhanced by the rising and falling concentrations of bouyant vor-
ticity from the heated and cooled walls. Boundary layer separation occurs immediately downstream from
these dominant circulations. The counter circulations so developed usually migrate along the horizontal
boundaries. Buoyant inhancement of the counter circulation is most likely in the vicinity of the lower
left and upper right corners where thermal boundary layers become stretched into plumes. In Fig. 2C
such a plume is evident near the left side of the lower boundary.
Measurement of the heat transfer in the transitional and upper range is difficult because the un-
steadyness can lead to wide extremes (numerically we cannot measure transfer right at the wall). Long
term averages must be taken. Currently we are still in the process of dealing with these measurements
along with necessary work that must be done on overall data reduction. For the calculation of Fig. 2A
(A = 10®, a = 1) we estimate N~32.0. Numerical programs to give late time average heat transfer values
have not been employed at this writing.
Finally we consider the last group (Fig. 3) in greater detail. The single circulation behavior of
the high Rayleigh number flows is somewhat of a surprise because here the character of the flow is al-
most the same for a very wide range of values of the parameters. Quantitatively the flows remain dif-
ferent particularly in the speed of circulation at late times or the rate at which the circulation speed
increases from the initial no flow state. In this range the viscous and conduction effects are essen-
tially absent at the central region but intense at the boundaries. The results show dramatically why
boundary layer theory has been so successful in manv theoretical studies of fluid flow. While the un-
steadyness far exceeds that of the transition range it is almost entirely confined to a thin layer at the
boundaries and to the corner regions. There is eccentricity in the flows that does not appear to di-
minish over the range of time covered by the calculations. An almost perfectly circular flow may be
disrupted by migrating corner activity. Such a disruption may lead to increasingly eccentric flow but
never a return to the type of flow of the transitional range.
In these flows it is not uncommon for plume roll up to occur so that a hot or cold spot is carried
out into the main circulation. Once caught up in the main circulation it may undergo several revolutions
before intermingling again with the thermal boundary layer or getting trapped in a comer of the flow
region .
The single circulation behavior must be a consequence of the very low dissipation and slow conduc-
tion process in the interior flow region. In the absence of some roughness or protrusion from the boun-
dary to inhance mixing the interior region remains isothermal. It is also free of vorticity because
boundary generated vorticity does not penetrate to the central region and the isothermal fluid does not
contribute buoyant vorticity.
Early transitional behavior from the no flow initial condition does involve similar behavior to that
of the transitional range flows. It may however be of value to investigate the effects of the initial
state. Presumably late time solutions for an initial state of the interior fluid at the cold temperature
would ultimately be the same as the given solutions of Fig. 3, but no calculations of this type were
made .
In Fig. 3A we note that counter circulations to the main circulation are very limited. The apparent
smooth appearance of this still shot is not indicative of the actual behavior. Small extremals of vor-
ticity (Fig. 3B) or hot spots of temperature (Fig. 3C) that occur on occasion in the central part of the
flow have been timed to estimate a mean speed of the main circulation. In an 8 ft. square enclosure
the circulation time is roughly 5 seconds. This is not unreasonable but much work still needs to be done
in comparing our results with experiment. It is uncertain to what extent the numerical result provides
for the mixing that Would occur in the turbulent flows as observed in the laboratory.
5. Acknowledgements
The author wishes to acknowledge the assistance of Donald E. Schreiber^° whose graphics programs for
the IBM made it possible to reduce many numbers to very meaningful pictures. Acknowledgement is
also due William E. Langlois for his review and recommendations of the work.
6. Refe
[1] Foots, G. , "Heat Transfer by Laminar Free
Convection in Enclosed Plane Gas Layers",
Quart. J. Mech. App. Math., 11, 257-273 ().
[2] Wilkes, J.O. , "The Finite Difference Compu-
tation of Natural Convection in an Enclosed
Rectangular Cavity", University of Michigan,
Ph.D. thesis ().
nces
[3] Deardorff , J.W. , "A Numerical Study of Two-
Dimensional Parallel Plate Convection", J.
Atmos. Sci. 2_1, 419-438 ().
[4] Fromm, J.E., "Numerical Solutions of the
Nonlinear Equations for Heated Fluid Layers",
Phys. Fluids 8, 175 7- ().
458
Aziz, K. , "A Numerical Study of Cellular Con-
vection", Rice University, Department of
Chemical Engineering, Houston, Texas ().
Roberts, K.V. and Weiss, N.O. , "Convective
Difference Schemes", Math. Comput. _20, 272-
299 ().
Fromm, J.E., "Practical Investigation of Con-
vective Difference Approximations of Reduced
Dispersion", in High-Speed Computing in Fluid
Dynamics, International Union of Theoretical
and Applied Mechanics Symposium, American
Institute of Physics, New York, New York ().
[8] Marchuk, G.I., "The Automatic Construction of
Computational Algorithms", translated by G.J.
Tee, Technical Report CS30, Computer Science
Department, Stanford University, .
[9] Bunemann, 0., "A Compact Non-Iterative Poisson
Solver", SUIPR Report No. 294, Institute of
Plasma Research, Stanford University, Stanford
California ().
[10] Schreiber, D.E. , "A Generalized Equipotential
Plotting Routine for a Scalar Function of Two
Variables", IBM Research Report RJ 499 ().
459
Appendix
In this appendix we describe the form of the convective approximation used in the calculations. We
shall give the form of the flux term in the u direction only, but for the various ranges of a = uAt/Ax
as indicated earlier. It must be remembered that the flux as given is only half of the required compu-
tation for a given mesh point . If the flux is added to the point on the right and subtracted from the
point on the left the speed of computation can be reduced by half. Also the same convective program
can be used for both vorticity and temperature if these variables are defined the same relative to the
grid. The fluxes in the vertical direction may be inferred from those given here for the horir.ontal .
We define
u , At V. , . At
a. ^ ,„ . = T — ■' and S. , . = ; — •'
1-1/2, J Ax 1-1/2,3 Ay
where
Vi/2,j = ^*i-i,j+i + '^i,j+i - "^i-i.j-i - *i,j-i^ /
^-l/2,j = ^"^i-l.J-^.j^ /
If |a|<.09 we use an upstream second order approximation. We here write the central approximation
terms with the understanding that if a>0, a is replaced by (a-1) and i indices are reduced by 1.
Further if a<0, a is replaced by (a+1) and i indices are increased by 1. To make addition and
subtraction of flux contributions possible as previously mentioned the powers of a must further be
modified. For example must be replaced by [(a-l)^-l] = a^-2a so that Eq. (11) does indeed
apply without a shift of index on the leading term of this equation. Cancellation of the appropriate
linear terms (terms that do not contain a) can readily be varified for the difference forms here given.
This however requires writing out the complete expression of both the flux into and out of the cell of
interest .
Define
_ = T. , . + T. . , D. - = T. , . - T. .
3,0 1-1,3 1.3 3,0 1-1,3 i.J
^6,2 ^i-1,3+1 '^1,3+1 ' °6,2 ^i-l,j+l ^i,j+l
and . = T. ^ . , + T. . . , D_ ,= T. , . , - T. . ^
7,4 1-1,3-1 i>3-l 7,4 1-1,3-1 1)3-1
Here the subscript numbers follow a procedure of successively numbering points in a counter clockwise
direction starting with the point just to the right of a point of interest. The symbol Ci,3) and the
symbol 0 are synonymous.
Now with index i-1/2 implied for a, 3 and F we write
7^ F = 1/2 a S- . + 1/8 a6(S, , - S, ,)
Ax 3,0 7,4 6,2
+ 1/2 a2 Q + 1/12 aB2(s^ ^ - 2 ^ + 2^
+ 1/6 a2g(D^ 4 " °6 2'' -"-^^ a^e>^(D^ ^ - 2 ^ + ^)
For 0.9 <^ |a| _< .5 we use a fourth order upstream expression and for .5 < |ci| 1 we use the
average of the upstream and central expressions. Here again we give only the central difference ex-
pression. The same rules apply on replacment of a appropriately with (a-1) or (a+1) and shifting
indices as previously indicated.
Define in addition to the above sums and differences
460
T.
+ T. , D.
= T.
- T.
15,10 i-l,j+2 i,j+2 ' 15,10 1-1, j+2 i,j+2
T.
+ T
= T.
- T. .
18,12 i-l,j-2 i,j-2 ' 18,12 i-l,j-2 i,j-2
T. „ . + T.
T.
11,1 i-2,j ,i+l,j ' 11,1 i-2,j i+l,j
T.
+ T
. = T,.
- T.
16,5 i-2,j+l i+l,j+l ' 16,5 i-2,j+l i+l,j+l
T.
+ T
T.
- T.
17,8 i-2,j-l i+l,j-l ' 17,8 i-2,j-l i+l,j-l
= T
+ T.
22,14 i-2,j+2 i+l,j+2 ' 23,14 i-2,j+2 i+l,j+2
and
T.
+ T
T.
T.
23,19 i-2,j-2 i+l,j-2 ' 23,19 i-2,j-2 1+1, j-2
We may now writejwith index 1-1/2 implied for a, 6 and
42
Ax
E
1=1
Where the B's and X's are given in Table II (A and B) , and the numerical coefficients associated
with the B's are given in Table III.
Table II-A. Leading terms and differences of fourth order approximation.
B
X
1
11 a
^3,0
2
^21 "
^11,1
3
^11^11 °
6/2
^7,4 -
'6,2
4
^11^21 <^
S/2
^18,12
" ^6,2 " ^15,10
5
^21^1 "
6/2
^17,8
" ^16,5
6
^21^21 "
6/2
^23,19
" '17,8 ^16,5
" '12,14
7
8
^2
A22
^.0
°11,1
9
^11^12
6^/3
'7,4 -
2^3,0+^6,2
10
^1^22 °
62/3
^18,12
- ^7,4 - ^6,2 +
'15,10
11
^21^2 °
62/3
^17,8
12
"^21^22
e2/3
^23,19
" ^17, 8 ~ ^16,5
+ '22,14
13
2 A A
^^12 11
a2B/3
°7.A -
°6,2
14
2A^2'^21
a^B/S
°18,12
- °7,4+ '^6,2 -
°15,10
15
2^22^11
a26/3
°17,8
- °16,5
16
2^22^21
a26/3
^23,19
- °17,8+ ^^16,5
~ ^^22, 14
17
A23 a3
X2 - X
1
461
Table II-A. continued.
B
X
18
A A
11 23
4 3
19
^21^23
^6 - S
20
^12^12
°7,4 - 2^3,0 +
21
A A
12 22
a2B2/2
°18,12 ~ °7,4 "
■ \,2 +
^15,10
22
^22^12
a2B2/2
°I7,8 -
^ ^16,5
23
^22^22
a2B2/2
^^23, 19 ~ ^17,8
- °16,5
+ °22,14
Table II-B. Leading terms and differences of fourth order approximation, (continued)
B 1
X
25
■^^23^11 "^'^^^
3A„,A., a36/4
23 21
■ S - ^3
26
^24
Xg - 3X^
27
28
^11^24
A„A-, oB'^/S
21 24
^12 -^^11
29
30
2A, .A„. a2B3/5
12 23
2^22^23
^4 ~ ^13
^16 " ^15
31
32
■^^23^12 '^^^^^
3^23^22 "'2/5
hi ~ ho
33
34
^^24^11 ""^"^^^
^"^24^^21 "^^/^
h5 " ^^13
h6 ~ ^^14
35
36
A^2A24 "23^/3
^22^24 "^^''''3
^21 " -^^20
X23 - 3X22
37
A23A23 a3B3/2
^19 " ^18
38
39
2A2^A^2 ""^S^/S
2^24^22 "'''^^''3
^22 " ^^20
X23 - 3X2^
40
3A2 3A2^ a 334/7
^28 " ^27
41
4A2^A2 3 a'*s3/7
X30 - 3X25
42
^24^24
^36 " ^^35
462
Table III. Coefficients of fourth order approximation.
^1
7/12
hi
15/24
- 1/12
- 3/24
^21
- 1/12
^22
- 1/24
^2 3
1/12
^24
1/24
Figure lA. Steady streamxme solution for A = 10^, c = 1.0. The plot increment Aij; = 0.05ft^/sec.
i/j = 0 at the boundary and 0.025 at the first contour from the boundary.
Figure IB. Contours of constant vorticity for A = 10^, a = 1.0. The plot increment Ao) =0.2/sec. The
minimum displayed contour value is -0.5 and is the inner contour of the two symetric ex-
tremals, oj maximum at the wall is 2.47.
Figure IC. Isotherms for A = 10^, a = 1.0. The plot increment is AT =0.5°F for the overall wall tem-
perature difference T - T = 10.0.
453
Figure 2A. Late time streamline solution for A =10^, a = 1.0. The plot increment Atjj = 0.02£t2/sec.
The separation streamline ijj = 0 is given and is the reference contour.
Figure 2B. Vorticity contours corresponding to Figure 2A. Ato = 0.75/sec. u maximum at the wall is 12.9.
Figure 2C. Isotherms corresponding to Figure 2A. AT =0.5°F.
Figure 3A. Late time streamline solution for A = 10^^, a = 1.0. The plot increment Aijj = l.Oft^/sec.
The separation streamline i|; = 0 is given and is the reference contour.
Figure 3B. Vorticity contours corresponding to Figure 2A. Aoi = 10.0/sec. co maximum at the wall is 145.4.
Figure 3C. Isotherms corresponding to Figure 2A. AT =0.5°F.
464
Fortran IV Prograxn to Calculate Absorption
and Transmission of Thermal Radiation by
Single and Double-glazed Windows
G. P. Mitalas and J, G. Arseneault^
Division of Building Research
National Research Council of Canada
Ottawa
In the calculations of the heating or cooling load for a room,
it is necessary to know the fraction of the solar radiation incident
on the outside of the window that is absorbed by the glass and the
fraction that is transmitted to the interior of the room. This pro-
gram calculates the absorptivity and transmissivity of windows
made of common glass. In addition the coefficients for a 5th degree
polynomial are calculated to allow rapid (although less accurate)
determination of these factors for a given window and given incident
angle of solar beam.
The calculations by this program are based on:
(a) Fresnel's formulae (relation between incident angle, refraction
angle and reflection of parallel and perpendicular polarization
components of radiation).
(b) Snell's law (relation between refraction and incident angles).
(c) Exponential extinction law (relation between glass sheet thickness,
extinction coefficient for glass and absorption of radiation in a
single pass).
The calculated factors for single and double glazed windows
account for the multiple reflections and absorptions that occur when
radiation passes through more than one air-glass interface.
The 5th order polynomials, that relate the factors and the
cosine of incident angle, are fitted by the least-squares method
using the calculated values for incident angle 0° to 90° in one degree
steps. The coefficients of these polynomials are used to calculate
diffuse radiation factors assuming that the diffuse radiation from
the sky and the ground has equal intensity at all incident angles.
Key Words: Absorbtion, glass, radiation, solar trans-
mission, window.
Research Officer and Computer Systems Programmer, respectively.
465
1. Expressions for Absorptivity and T ransmis sivity of a Window
The single air-glass interface reflectivity is given by Fresnel's formulae
tan^ (9^ - e^)
" tan (6^ + e^)
sin^ {9^ - 9 )
sin (9^ + 9^)
where r // and r^ = the reflectivity for radiation that is polarized with the electric
vector parallel and perpendicular, respectively, to the plane
that contains the incident beam and a normal to the interface.
1
The refraction angle is related to the incident angle by Snell's law.
incident angle
refraction angle
Sin 9^ = n Sin 9^ (3)
where n = index of refraction for the glass.
For normal incidence 9 = 9^ =0
2
fn - W
^""^ 7/ \
The fraction of the radiation that is absorbed in a single pass through a glass sheet of thickness
L. is given by
a = 1 - exp (-KL/Cos 9^) (5)
where K = extinction coefficient for glass.
The absorbtivity. A, transmis sivity, T, and reflectivity, R, of a sheet of glass and double-
glazed window are calculated for parallel and perpendicular polarization separately. The average
values of A,, and A , 1 , , and T , or R// and R are applicable for non-polarized incident beam.
The factors A, T, and R of a single sheet of glass (taking account of multiple reflections of
both surfaces and multiple absorbtions) are given by
A . a(l - r) [1 + r(l - a)]
1 - r^ (1 - a)^
466
(1 - r) (1 - a)
1 - (1 - a)^
(7)
and
R
r +
r(l - r)^ (1 - a )^
2 2
1 - (1 - a)
(8)
where r and a are the single pass factors. The factors for parallel and perpendicular polarization
components are calculated when r - r jj and r = r respectively.
The double-glazed window absorptivity, ^-^-q ^'^'^ ^ZH' ^^'^ transmis sivity, T^^, are given by
2D
1 - R^R^
(9)
ID
^1 ^2
1 -R^R^
(10)
and
^1^2
"D
1 - R^R^
(11)
where the quantities with subscript D are for double-glazed windows and those without subscript D
are for a single sheet of glass. The subscript 2 denotes the factors for the outer pane and subscript
1 refers to the inner one.
2. Polynomial Coefficients
The 5th order polynomials, that relate the factors and the cosine of incident angle, are fitted
by the least-squares method. For example, the polynomial that relates A and cos 9 , is
A
I
C , . (cos
A, 1
(12)
where ^ = calculated polynomial coefficients for an absorbtivity A.
Polynomials are fitted only to the non -polarized beam factors using the calculated values for
= 0° to 90° in one degree steps.
3. Diffuse Radiation
For heat -gain calculations through a window it is usually assumed that the diffuse radiation
from the sky or the ground has equal intensity at all incident angles. The factors for diffuse radiation
of this nature are given by
n
/2
F = / F(e ) sin 29 d9 (13)
diffuse
467
where F(9) is the factor for direct solar beam and is a function of the incident angle 6. The substitu-
tion of the polynomial e;fcpression for F(6) and integration gives
5
F
Ci
(14)
diffuse
i + 2
where
Ci
5th order polynomial coefficients that relates the factor F and
cos 9 , .
4.
General Description of the Program
This Fortran IV program is for an IBM -System/ 360 operating system.
The coding sheets, a sample of output and the flow diagram (fig. Al) are given on pages A-1 to
A -7 of Appendix A.
Input:
Card 1 - columns 1-10 n, index of refraction
Card 2 - columns 1-10 KL inside
1 1 -20 KL outside.
Format: Floating point, 10 columns.
This paper is a contribution of the Division of Building Research, National Research Council of
Canada, and is published with the approval of the Director of the Division.
468
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469
start
200
Print
input
data
Set
Calcul.
1 W
►
01=0
►
Cos 01
— 1
Calcu late
Aj, 1 , A2, II
T2 , II , Rj, 1 ,
"z- II
A| , 0 . Aj, 0
and To
30
Calculate
C't s for
A I and T
KL out
*0
KL outN
= 0
Calcu late
A|,i , A|, ii,T|,x
T| , II , R I , x . R i . II
T| and A,
Calculate
C'lS for
A2
Print the factors
for selected
incident angles
\8,t^0
30
Calcul.
rii and
r,
KL out = 0
Calculate
C, s for
R
180
Calcul.
diffuse
rad.
factors
KL out = 0 Indicates single glazed window
Print Ct s
and diffuse
rad. factors
Figure Al - Flow Diagram for Absorption and Transmission Factor Calculation Program.
470
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476
A Computer Analysis
of Window Shading Coefficients
ty Calculating Optical and Thermal Transmission
E. Isfalt
The Royal Institute of Technology
Stockholm
Measurements of solar heat gain through windows with different shading
devices are rather complicated and need a calorimeter or some other kind of
expensive equipment. The optical properties of a single layer can be found
quite easily by spectrometer measurements in a laboratory. The paper describes
a method to calculate the solar heat gain through combinations of layers
outgoing from the optical data for the single layers. The ALGOL-program
developed to solve this problem allows an arbitrary number of layers, anyone
could be diffusing. The direct and total transmission through the combination,
the reflexion, and the shading coefficients eire calculated. The results of
a theoretical investigation of different window combinations are presented.
Key Words: Artificial lighting, daylighting, daylight distribution,
fenestration, light transmission, polarization, shading coefficient,
shading devices, solar heat transmission, soleir optical properties,
solar radiation, window shading coefficients.
1 . Introduction
For a correct choice of shading devices many different aspects should be taken into consideration.
Apart from the solar heat reduction, illumination demands, glare, operating possibilities, dirtying,
sound, aesthetical demands etc. should be paid regard to. In most cases these points of view should
be taken into account at the lowest possible cost. Information on shading devices is often restricted
to values of the solar heat reduction. Below it is indicated how calculations of the transmission
of sunlight as well as solar heat can be made starting from optical data for the different layers
of a window. Thereby it is possible to determine the heat flow into a room with regard to solar heat
and artificieil illumination.
2. Concepts and Definitions
The optical properties of a translucent layer is indicated by its transmission, T, reflexion ,R,
and absorption. A, of incident radiation. For these quantities the following is edways applicable
T + R + A = 1
The optical properties are due to the wave-length of the radiation. Solar radiation is within a reinge
of wave-length with a certain distribution within this range.
On calculations of this kind it is presupposed that the optical properties are average values
for solar radiation, i.e. they are valid with regard to the distribution of wave-length of the solar
radiation and the properties of the layers (Solar-Optical Properties).
The part of the incident radiation which is absorbed, part A, causes a heating of the layer.
Hereby part of A will be transmitted into the room by long-wave radiation and convection, the secondary
transmission.
Thus the solar heat transfer through a window consists of two parts, the direct and the secondary
transmission.
The direct and total transmission is due to the angle of incidence of the radiation. For most
window combinations curves of almost the same appeEirance are applicable. The curves diverge approxi-
mately by a constant factor. This implies that the transmission of a certain window can be related to
477
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m , ^ = m + m. + m.
tot y f 1
From these equations , q^, t^ and t^ are eliminated and the secondary transmission is obtained from
the expression
t^ - t^ m m +
Sec" m^ ^ ^1(2) ^ ^(1)2 * m, ^
tot tot tot
Here the first term constitutes the heat transmission owing to the difference of temperature between
the outside and the inside, the other terms aire contributions from absorbed solar radiation.
Similar derivations can be made for several layers . It can be observed that the inward-flowing
fraction of the absorbed radiation in a layer is always the ratio of the thermal resistance from the
layer to the outside air to the total thermal resistance of the window.
h. Arbitrary nmber of layers. Computer Program
The extensiveness of the calculations increases rapidly by the number of layers. The equations
for the course of radiation in the layer combination vary owing to where a possible diffusing layer
may have its position. Instead of using different equations for different cases when calculating with
a computer the radiation components are followed and added successively until all contributions are
exceedingly small.
The core of the ALGOL-program which has been drawn up for these calculations consists of a
procedure which divides the radiation components at each layer into one transmitted, one reflected
and one absorbed part. The radiation components are stored in a two-dimensioned array
IN [from, to]
The layers are numbered 1, 2, 3 etc... NUMBER from the outside. (Capital letters for identifiers).
The calculations proceed by steps forwards and backwards through the window. At each step one element
is divided up according to the pattern below
ATOT [1] ATOT [2] ATOT [3]
+ + +
etc. ■«- In[2,1] ♦in [1,2] ■* m[2,3]-* etc.
etc. etc.
When the radiation has passed through or has been reflected against a diffusing layer the optical
properties of the different layers which are stored in the arrays T NR , R NR and A NR are
exchanged for the values applicable to diffuse radiation.
The direct transmission constitutes the sum of all elements IN [NUMBER, NUMBER + 1]
and the reflexion the sum of all elements IN [1 , o] .
When the calculation has proceeded so far that all contributions are smaller than a given tolerance,
the direct transmission, the reflexion amd the absorption in each layer are summed up. This sum should
be = 1 . Finally the secondary transmission is determined with the aid of the thermal resistances which
were given as data and the calculated values of the absorption in the different layers.
478
the transmission through a reference window and thus be characterized with the aid of one single factor
which is independent of the angle of incidence. This factor is called the Shading Coefficient.
If the solar radiation values are determined once for all with regard to the reduction in the
reference window the angles of incidence of the solar radiation need not be determined any more.
In Sweden an unshaded two-glass window of ordinary window-glass is used as a reference. (The total
transmission when the radiation is falling in perpendicularly = 0,79).
The directly transmitted short-wave radiation and the secondarily transmitted solar heat are
distributed in different ways in a room. The short-wave radiation is reflected between the room-surfaces
whereas the long-wave radiation broadly speaking interprets the room-surfaces as being black. When
calculating with our main program [2] this difference is taken into consideration. For this reason
two shading coefficients and F^ have been introduced: F^ mxiltiplied by the incident solar radiation
through the reference window gives the totally transmitted solar heat, F similarly the directly
transmitted part. If the spectral changes of the radiation are small at the passage through the window,
Fg is a value of the light transmission.
3. Double panes
3.1 Short-wave radiation
When several layers are combined they affect each other by reflexions between themselves. The
course of radiation when there are two translucent layers can be seen in Fig. 1, in which the denomi-
nations used below are also given. The repeated reflexions give rise to geometrical series, the sums
of which are included in the following expressions:
The direct transmission is achieved from the expression
T • T
1 2
■12 1 - •
The reflexion
2
T • R
1 2
'12 " "1 ■ 1 - •
R,^ = R, +
The absorption in layer No. 1 with contribution of layer No. 2
T • R
^(2) = \ ' 1 -'r^ \ )
The absorption in layer No. 2
A,
^1 • ^2
(1)2 1 - R^ . Rg
3.2 Long-wave radiation and convection
The secondary transmission can be derived from Fig. 2.
For the denominations introduced in this figure the following is applicable
t = temperature
m = thermal resistance
q = heat flow
The heat flows are given by
y
479
5 . Applications
3•^ Influence of polarization
As to calculations including several panes the effect of the polarization is often taken into account.
This is not the case in this program. Fig. 3 shows the direct transmission through a two-glass window
determined with as well as without regard to the polarization. It is evident that the imperfection
is not noticeable until the angles of incidence are larger than about kO . If the determination of
and F^ is made with layer data valid at an angle of incidence of for instance 30 the imperfection
is negligible.
5.2 Different nijmbers of panes
The availability of the program is first illustrated by the following example:
Calculations with the number of ordinary window-glasses (T = 0.86, R = 0.079) increasing from _^
2 to 6 have been made. Thermal resistances: outside 0.06, inside 0.11, between glasses 0.17 m^ °C W
Fig. k shows the result. The secondary transmission increases by the number of glasses. The direct
transmission, however, decreases more so that the total transmission decreases by £in increasing
number of panes.
5.3 Windows with drapes
The optical properties of a drape fabric is variable within wide limits owing to the fact that
the closeness of the texture as well as the color of the fabric can be varied. Calculations have been
made for varying types of drapes in combination with two panes of ordinary window-glass (T = 0.86)
placed on the outside, between the panes and on the inside. The direct transmission indicated by Fg,
is supposed to be the same for visible light as for radiation in the whole solar spectrum. Since
the primary purpose of the window is to let in the daylight it is natural to start from F^ as an
independent variable, which is the case in the figures 5-7. The total transmission indicated through
F^ is a dependent variable and T and R of the drape fabric are parameters.
The following values of heat resistance in °C W ^ have been used:
outside 0.06
inside 0.11
glass to glass 0.17
glass to drape 0.13 when drape outside, else 0.15
6. Utilization of calculated data
The following example is intended to illustrate how the values which are achieved from the
diagrams can be used in a chain of calcxilations concerning the heat flow into a room due to sun and
illumination.
6.1 Assumptions
The example refers to a room with the dimensions
breadth = 2.5 m
depth = l+.O "
height = 2.9 " 2
window area = 3>Zh m
Other pre-requisites :
latitude 60°N
orientation South
climate August, clear day
Window: drape between 2 ordinary window-panes
The shading coefficient F^ = U0%. This value is achieved according to Fig. 6 for instance
with combinations according to the table below.
480
Fabric Transmittance % Fabric Reflectance % %
11 38 10
21 50 20
29 60 30
The value of F^ is decisive for the daylight in the room. Owing to the demands of illumination
Fg therefore is determining for the heat energy from artificial illumination.
6.2 Solar radiation
through the refere
determined by a program from information about latitude, longitude, date and orientation
_2
The incident solar radiation, in ^fei , through the reference glass (unshaded double glazing) is
6.3 Visible radiation
The sunlight is supposed to be in keeping with the incident solar radiation and is indicated by
a luminous efficiency factor.
6.3.2 Distribution of daylight
The distribution of daylight in the room is achieved with the aid of a program which determines
the absorption factors for radiation from the window against horizontal surface elements placed
arbitrarily in the room. The calculations thus presuppose a diffuse distribution of the light. In the
result an infinite amoiont of reflexions between the room surfaces is included.
For the room in question the program gave the following values of the ratio of the lumance of
the window surface to the daylight illumination along the central line of the room at a height of 0.8 m
Distance from window, m ratio
1 0.212
2 0.108 (middle of room)
3 0.068
6.k Artificial lighting
The calculations made so far have given the incident solar radiation and the daylight hour by hour
in the room. Fig. 8 shows the incident solar radiation in W m"^ window area and the illumination in lux
in the centre of the room for = 10, 20 and 30^.
The consequence of different demeinds of illumination in the centre of the room can now be examined.
The calculations concern the time between 8 and l6. When the daylight is insufficient it is pre-
supposed that the illumination is switched on. With different demands of illumination Fig. 8 gives the
following illumination periods for different values of F^
Artificial lighting, hours
Lux
^2
500
10
3.5
8.0
8.0
20
0.5
3.5
8.0
30
0
1.1*
3.5
6.5 Total load
Provided that the armature gives 20 lumens per watt the energy with which the room is supplied
from sun and illumination during the day gets the following values:
Energy from sun and
artificial lighting, W h
Lux
^2
500
10
20
1
30
481
On the basis of these values Fig. 9 has been drawn. The figure shows the great importance of
considering the light as well as the solar heat transmission when choosing shading devices. The heat
load as a result of sun and illumination at a demand of illumination of lux is about 30% larger
for a drape with F = 13% than for one vrith F = 30%. The incident solar heat is the same in both
cases (F^ = kO%) .
References
ASHRAE Handbook of Fundamentals, Ch.
pp U67-512 ()
XXVIII
Brown, G., Simulation by digital computer
program of the temperature variation in
a room. Contribution to this symposium.
482
M(2)
1-1
jtdoor
indoor
^sec
M(2)
Hm
'sec
2. Denominations used to derive the secondary
trajismission through a two-glass window.
transmittance , %
80
60
40
20
0
■
ith regard to |
polarization
without reg<
3rd to polariz
3tion\\
\
0 20 40 60 80 ' 100
angle of incidence
3. Direct transmission through a two-glass
window determined with as well as without
regard to the polarization.
483
1.0
I
total transmission
secondary trans- _
mission
I I I
Total and secondary transmission through
different numbers of panes.
5 6
number of panes
' 1
1.0
Shading coefficient F (for total
transmission) as function of
coefficient (for direct trans-
mission) for double glazing with
drapes. Drape solar optical
properties are parameters.
0 V. 1 1 1 1 1
0 .2 .4 .6 .8 1.0
F2
484
4 000
10
20
F,-40%
30
40
486
Optimum Shape of External Shade for the Window
to Minimize Annual Solar Heat Gain
and to Maximize View Factor
K . Kimura
Department of Architecture
Waseda University
Tokyo , Japan
One of the most fluctuating components of space cooling load
is associated with solar heat gain from windov/s . Overhangs, side
fins or screen type of sun shades are v/idely used to avoid unwanted
heat from the sun. On the other hand the windov/ is expected to
provide sunlight into the occupied space and allow people to look
outside through it. Considering that the design of shading devices
should be coordinated to both of these factors in conformity with
aethetics , the author developed a procedure to determine the
optimumshape of external shade for a rectangular window of a given
proportionfacing to a specified orientation so that it could inter-
cept direct radiation as much as possible and be fabricated with
a minimum amount of material, providing a maximum possible view for
the occupants. Iteration process is required to obtain the geometry
of the sun shade composed of two pairs of horizontal and vertical
flat plates with optimum width and tilt angle. This is follov/ed
by the estimation of the annual total solar heat gain from the
window with the brise-soleil thus designed, talving account of
reflection and re-radiation from sunlit surfaces of sun shade as
well as direct and diffuse solar radiation transmitted through the
shade. The heat exchange problem around the shade assembly is
approximately solved by the method similar to that to calculate
the weighting factors relating heat gain to cooling load. The
routines developed are intended to be incorporated with graphical
display system or plotter drawing system so as to be an effective
aid for the architectural design.
Key Words: Computer, optimization, brise-soleil, windov/,
solar radiation, shadow, overhang, side fin, view factor,
heat gain , design .
1. Introduction
Design of sun shades for the building fa9ade is one of the most interesting phases
of architectural design associated with environmental engineering. In determining the
shape of sun shades the designer wants to Ivnow the actual effects of shading devices in
terras ofannual energy savings owing to the reduction of solar heat gain as well as the
cost to fabricate it. It is considered necessary, therefore, to offer the designer the
optimum range of key elements defining the geom.etry of sun shade so that he can determine
the shape of it with his idea and aethetical judgement, eliminating such unnecessary
steps that he has to draw many figures of obviously ineffective sun shades. Determining
the shape, the computer can calculate the cooling load for air conditioning engineers as
well as the manufacturing cost to justify the installation of sun shades.
Conventional architectural design involves various phases of design process such as
v/orking on drawings, refering to informations, mailing discussions and so on. In order
to use the computer as a design partner the design procedure must be systematized aiid the
design operations be performed in a logical flow without losing artistic inputs. This
"Associate Professor, Department of Architecture.
487
is the general concepi; of computer aided design and the attempts made on the sun shade
design is based on it.
2. Basic Concept
2.1 Design Process and Use of Computer
The process of architectural design is too complexed to be thoroughly systematized,
but efforts are being made by computerists to seek the possibilities how far the design
process can be computerized taking various human factors into account. This approach is
being attempted by Negroponte (1)-^ and his colleagues in their program development for
urban design. For simplicity in this paper it is presupposed that the design process is
composed of the combination of various minor processes and they may be either inductive
or deductive depending on situations.
It is considered that the conventional process of architectural design consists of
multiple repetitions of making decisions based on various requirements and designer's
idea and judgement through the routines of deriving effects caused by the decision and
checking conflicts ajnong other decisions in reference to the design criteria. This is
shown on the left side of Fig. 1, Since it is always advantageous to use computer when
calculation involves a number of repetitive routines, the design process v/ith computer
should be so arranged as to include repetitive routines. The right side of Fig, 1 shows
a flow of the deductive design process where the computer gives a number of answers that
meet the requirements and suffice the criteria and the designer only has to select one
out of them based on his idea and judgement. If the computer gave only one answer, which
might be the most optimum, there would be no room for selection. It is desirable, there-
fore, that the optimum range of key elements defining the object should be provided,
because the most optimum one may be much inferior to another v/hen refered to the design-
er's idea.
On the other hand conversational or on-line type of design process with computer,
which might be called inductive design process , can go through the same routine as the
conventional one as shovm on the left side of Fig. 1 again. When the graphical display
system ;vere used, for example, the calculation of checking conflicts and deriving effects
can simultaneously be made by the main processor and the designer can change as many
decisions as he likes while sitting down at the C.R.T. console.
2.2 Basic Approach to Design of Sun Shades
The object problem for sun shade design presented in this paper is to determine the
optimum shape and to calculate heat gain from windows excluding the cost estimation rou-
tine. The overall phase of it is shown in Table 1 in the list up form of input and out-
put items ,
Table
1. Input and output
of object
problem
I/O
Description
Symbol
Item
Unit
Location of building
LAT
LONG
Latitude
Longitude
degrees
degrees
Input
Wall orientation V/0
Shape of v/indow to which B
sun shade is to be attached
Normal direction to wall
surface
Proportion of v/idth to
height of window
degrees
from south
Design criteria
PSA
Upper limit of sunlit area
per window area
Optimum Shape of sun
shade
DL
Projection of overhang per
windov/ height
FL Projection of side fin per —
windov; height
Figures in brackets indicate the literature references at the end of this paper.
488
Output
Reference data
AA
AB
AM
AS
VF
HG
Tilt angle of overhang
Tilt angle of side fin
Drav/ings
Area of material per
window area
Sunlit area per
windov; area
View factor
Heat gain through
fenestration
degrees
degrees
watt/mp or
kcal/m h
Table 2 shows the overall flow of the object problem subdivided into three phases
for the conversational type of design process in the sequence form of execution routines,
v/here Enter means to enter the input data at the keyboard and Xeq. means to execute the
calculation routine marked after that. These three phases also can be applied to the
deductive design process v/hich does not necessarily require C.R.T. console or terminal
units ,
Table 2. Sequence of execution routines
Phase
Operation
Output
I
Enter
LAT,LONG,WO
Xeq.
MAXSOL
IDV Maximum direct radiation upon window
TIMAX Time when IDV occurs
TPM Tangent of profile angle at TIMAX
TGM Tangent of wall solar azimuth at TIMAX
II
Enter
B, PSA
Xeq.
SHAPE
DL, FL, AA, AB
Drav/ings
Xeq.
REFER
AS, AM, VF
III
Enter
TIME
Xeq.
DSOLT
IDVT Direct solar radiation transmitted
through shade throughout the year
Enter
IVEATA (weather data)
Xeq . HGAIN
RDT Direct radiation transmitted through
shade and glass
RFT Diffuse radiation transmitted through
shade and glass
HTTR Overall heat transfer at inner surface
of fenestration
*MAXSOL, SHAPE, REFER, DSOLT, HGAIN are the back-up routines the programs of which
are loaded in the main processor.
The basic approach to the problem to find the optimum geometry of sun shade is, first
of all, that the sun shade should be designed so as to intercept the direct solar radia-
tion as much as possible v/hen it amounts to its maximum for the orientation to which the
window is faced. It would not be probable that the total solar radiation transmitted
489
through the window plus the heat gain associated with outside air temperature at other
times of the year would exceed the rate when the maximum radiation occurs, but this must
be checked before the decision is made.
5. Description of Routines with Example Results
3.1 Phase I
According to the above basic approach, the objective of Phase I is to find the
maximum rate of direct solar radiation upon the surface for the window orientation and
the sun's position relative to the v/indow surface when it occurs. Useful data on the
sun's position for the Phase II calculation are the tangent of profile angle as defined
by Parmelee (2) and the tangent of wall solar azimuth.
Example calculation results are shown in Table 3 for the window faced with south-
west and for the building located in Tokyo (35°41'N, 139°46'E). This shows the maximum
radiation occurs in January. Considering that the total cooling load usually amounts to
be higher in summer, the data for August were selected for the determination of optimum
shape of sun shade for Phase II calculation.
Table 3. Output data example of Phase I
Direct solar radiation Tangent of Tangent of
on vertical surface Profile angle wall solar azimuth
(kcal m~S-l)
January
1^
677.9
0.
0.
February
13
675.0
0.
0.
March
15
595.1
0.
0.
April
15
522.5
1.
0.
May
15
^81.2
1.
0.
June
15
3if2.5
1.
0.
July
15
385.4
1.
0.
August
15
455.3
TPM= 1.
TGM=0.
September
15
581.5
0.
0.
October
Ik
610.8
0.
0.
November
Ik
610.9
0.
0.
December
Ik
605.7
0.
0.
3.2 Phase II
The objective of Phase II calculation is to determine the optimum shape of sun shade
for a given rectangular window whose height is unity and breadth is B based on the output
information of Phase I. Studied in this paper is with an egg-crate type of sun shade
that consists of horizontal overhang and vertical side fins, both of which are made of
rectangular flat plates and may be tilted if desirable as shown in Fig. 2, where the
general shadow patterns are also illustrated. The design criteria adopted is the upper
limit of sunlit area of window when direct solar radiation reaches its maximum in summer.
The problem then is to find the optimum projection and optimum tilt angle of both over-
hang and side fins.
Fig. 3 is the flow chart showing the actual routines of Phase II calculation and
the followings are the step by step descriptions.
(1) Input data:
B = 0.5 ( v/idth of v/indow relative to height of windov/ )
490
TPM = 1.03if3/f ( tangent of profile angle at 3 pm in August, cf. Table 3 )
TGM = 0. ( tangent of v/all solar azimuth at 3 pra in August, cf. Table 3 )
PSA = 0.1 ( upper limit of sunlit area per v^indov/ area as design criteria )
(2) Initial set values of tilt angle of overhang and side fin:
AA = 0
AB = 0
(3) Calculate the tentative values of overhang projection DL and side fin projection FL
to have the sunlit area proportion AS made about 0.1 (PSA) v/ith the follov/ing formulas:
DL = 0.7 / ( tan AA + TPM ) (1)
FL = 0.7 / ( tan AB + TGM ) (2)
(4) Calculate sunlit area AS including the triangle area as shown in Fig. 2,
(5) Calculate area of material AM required per windov/ area as the sum of overhang area
and side fin area.
(6) Calculate view factor VF.
(7) Output data:
DL, FL, AA, AB, AS, AI'I, VF.
(8) Repeat calculation with the shape of overhang and side fin modified.
(a) Modify the tilt angle of overhang or side fin whichever gives larger shadow
area. Go to (3) .
(b) Modify the projection of overhang or side fin whichever gives larger shadow
area. Go to (4) .
Example calculation results for the window whose relative breadth to height B is 0.5
are shovrn in Table 4.
It can be seen that the area of material requires gets smaller as the tilt angles
of overhang and side fin increase , whereas view factor hardly varies regardless of the
shape as long as the sunlit area stays the same around 0.1 which is the specified- values
as design criteria.
All of these results shovm in Table 4 from the serial number I = 0 to I = 30 are
regarded optimum as far as the design criteria adopted is concerned.
Fig. if shows the plotter drawings of section and plan of the four selected types of
brise-soleil with the shadow pattern casted upon the v/indow , assuming that the designer
made his selection based on his idea and judgement to see the actual shape of them. In
Fig. Zf, (a) shows the figure of the type I = 0 in Table 4 , (b) I = 9 , (c) I = I9 and (d)
I = 29 • It would be more desirable to show the perspective drawings.
3.3 Phase III
Calculation of heat gain from the glass window combined with the sun shade the shape
of which is determined in Phase II is to be made in Phase III, There are three basic
components of heat gain that appear inside of glass: direct solar radiation transmitted
through shade and glass , diffuse solar radiation transmitted through shade and glass in-
cluding the reflected component from the sunlit surfaces of the shade and the heat trans-
fer from outside across glass including the long wave length re-radiation from the shade
surfaces the temperature of which could get considerably higher than the air temperature
because of the absorption of solar radiation. Fig. 5 shov/s the overall phase of direct
and diffuse solar radiation that turn out heat gain through the combination of shade
assembly and glass.
The direct transmission component can be calculated using SHADOW routines (3)}(4).
The diffuse component including the reflected radiation at the shadow surfaces can be
calculated with the view factor formulas. As the rigorous calculation of re-radiation
component is very complicated and attempts were made to simplify the situation and
estimate it in the form of equivalent temperature rise based on sol-air temperature
491
Table 4. Output data example of Phase II
B = 0.50
T
I
n 1
U L
^ A
A B
A S
AM
V F
A
\J
u . o o
0.72
0 . 00
0.00
0. 09
2.11
0.19
1
1
A 1
(1 on
U . 'J u
Cj . 0 9
1. 90
0.20
c
0. 74
0.61
0.00
5 . UO
C. 0 8
1.97
0.18
-3
I'l A ?
VJ . o ^
0.6 1
5.00
5.00
0.09
1.35
0.21
A
*+
V ^ . O 7
("i A 1
■i n fi
J . u u
^ n n
n 7
1 9 1
0 1 Q
C
U . o ^:
J . J J
*=i n n
T . u u
1 n nn
1 7 0
0 ? 1
o
U. O 7
J . LI U
in on
1 7 A
0) 1 M
f
U.JO
J . J J
in on
in nn
0 nq
1 . o6
■o.
0. 64
0.53
10.00
10.00
C . 07
1.72
0.19
Q
n ft
0.46
1 nn
15.00
G . 1 0
1.55
C . ? 1
1 n
i. \j
U . O
10.00
15.00
COS
1.61
0.19
X i.
0. 54
0.46
15.00
15.00
0.09
1.52
0.22
1 7
n . 5 9
0.46
15.00
15.00
C . 08
1.57
0.20
1
1 3
0.41
20.00
0.10
1.43
0.2 2
0. 59
15.00
20.00
C. 09
1.49
0.19
0.41
2 0.00
20 .00
0. 09
1.41
0.22
1 O
p. R S
J . ^ 1
7 T no
?c\ nn
0.08
1.46
0.20
1 7
1 f
0.5 0
Ti ^7
■J . J? (
2 0.00
2 5.00
0.10
1.34
0.2 2
1 ft
n s
U . J 3
fi ^7
? 1 nn
? n n
C . 0 8
0.20
1 Q
? s n n
0.09
1.32
0.23
C \J
n s 1
0,37
2 5.00
2 5.00
0.08
1.38
0.20
7 1
0 47
0.33
2 5.00
30 .00
C . 1 0
1.2^
0.22
n s 1
25 . 00
30.00
C. 03
1.33
0.20
2 3
0.43
0.33
30.00
30.00
0.10
1.26
0.23
24
0. 48
0.33
30.00
30.00
0 , 0 8
1. '31
0.20
25
0.43
0.2^
30.00
35.00
0. 10
1. 22
0.22
26
0.-^8
0. 2<;
30.00
35.00
C. 08
1.27
0.20
27
0. 40
0. 29
3 5.00
35.00
C. 10
1.21
0.2 3
28
0. 44
0. 29
35.00
35.00
0. Oo
1.26
0.21
29
0. 40
0.2 6
35.00
40.00
0. 10
1. 18
0.22
30
0.44
0. 26
33.00
40.00
0.0 7
1.23
0.20
Table 5. Output data example of Phase III
Time V/eather data
Direct Diffuse Outside
solar solar air
radiatn radiatn temp.
— (kcal m-2h-l)- degc
Output information
Direct Diffuse Keat
radiatn radiatn transfrd
transmtd transratd across
(kcal m-2h-l)
Squivalent temperature rise
Radiatn Re-radtn Atraosphrc
absorbed from radiatn
by glass shade
degC degc degC
_ 9
2
34
2u .c
0
10
3
49
29.6
0
11
?1
56
30.3
0
12
215
57
30.7
0
13
340
56
31.1
0
14
425
54
31.0
23
15
455
51
30.7
29
16
416
47
30.5.
1 r
-LO
17
288
39
29.6
0
18
54
22
23.4
0
11
7
0.16
0.19
-1.28
21
16
0.28
0.49
-1.30
29
23
0.39
1.05
-1.31
34
31
0.46
2.02
-1.32
37
39
0.51
3.19
-1.33
37
47
1.27
4.13
-1.32
35
50
1.42
4 . 7^
-1.32
30
47
0.91
4.91
-1.31
21
37
0.29
4.41
-1.30
7
22
0.10
2.94
-1.28
concept against the glass surface (5) using the weighting factor technique (6) as used
for space cooling load calculation. Detail of this approximation process is described
in Appendix.
Results of example calculation with the brise-soleil whose type is I = 29 in Table
4 are shown in Table 5. It can be seen that the re-radiation effect can be quite large
and the equivalent temperature rise aiaounts to over 7 degC especially when the shade
492
intercepts a considerable amount of incident solar radiation. The author's experiments
previously made (5) showed that the equivalent temperature rise was 3 - k degC at maximum
in summer.
In the process of heat gain calculation it is desirable to check whether or not the
shape of sun shade determined in Phase II could effectively reduce heat gain at other
times of the year as well as other hours of the month. It sometimes happens in winter
that the transmitted solar radiation amounts so high that one cannot control the space
temperature. Two methods to check the possibility of this situation throughout the year
are conceivable: one is to calculate only the direct solar radiation transmitted through
the sun shade because it is a predominant factor and the other is to calculate heat gain
or cooling load including other excitation components to make an overall judgement. If
the heat gain for any month turned out too much, the alternative shape should be selected
and the Phase III calculation repeated until the conditions regarding both aethetical and
thermal effects are satisfied. If it is still unsatisfactory, Phase II routine must be
repeated with input data revised from the results of Phase I calculation.
Z+. Conclusion
(1) As an example of optimization problem with computer the procedure to determine the
optimum shape of sun shade is presented. This is based on the realistical design process
so that an architectural designer could use his aethetical judgement in the course of the
computer calculation which could be combined with graphical display system or plotter
drawing system.
(2) The basic routines developed can be used both for the deductive and inductive design
processes by a simple application technique so that they could be an effective aid in
the architectural design of building fa9ade.
(3) The procedure to calculate the heat gain from the window v/ith brise-soleil talking
account of reflection and re-radiation from sunlit surfaces is also developed so that
the results obtained could directly be used for air conditioning load calculation.
5. References
(1) Negroponte , N,, Towards a Humanism through Machines, Technology Review Vol.71 No. 6,
Massachusetts Institute of Technology, April .
(2) Parmelee, G. V. and Aubele , V/. W. , The Shading of Sunlit Glass, ASHVE Transactions,
.
(3) Sun, T,, Shadov/ Area Equations for Windov/ Overhangs and Side Fins and Their Applica-
tion in Computer Calculation, ASHRAE Transactions, Vol.7i+ Part I, I968.
Groth , C. C. and Lokmanhekim , M. , "SHADOW", Proceedings of the Second Hawaii Inter-
national Conference on System Science, I969 , P.471-47A-.
(5) Kimura, K, , CoolingLoad Caused by Re-radiation from Sun Shade, Transactions of the
Architectural Institute of Japan, Special Issue, I965.
(6) ASHRAE Proposed Procedure for Determining Heating and Cooling Loads for Energy Cal-
culations, ASHRAE Task Group on Energy Requirements for Heating and Cooling, I968.
6 . Appendix
6.1 V/eighting Factors to Estimate the Heat
which is Discharged from Sunlit Shade Assembly
Part of incident solar radiation transmits through the shade as shovm in figure 3
and the remainder naturally falls upon the surfaces of the shade. Part of the radiation
absorbed in the shade material is once stored but eventually discharged to the air by
convection and to the glass surface by radiation, the remainder being emmitted to the
sky. The radiation component from sunlit shade surface to the glass is defined as re-
radiation and the effect of it can approximately be estimated using v/eighting factor
technique,
Refering to figure 6 the v/eighting factors W. relating the incident solar radiation
into the shade assembly to the heat discharged from all the surfaces of the shade can be
expressed by the following equations using the response factors of shade material X. and
493
Y^. Namely,
for j ^ 1 W = - ( X - Y )*a /a , (A-2)
J J J s so
where a is the absorptivity of shade assembly and OL is film coefficient along the
shade s§rface. ^°
Then HS the heat discharged from the shade surfaces per unit window area at time
t = ni\t, where At = time interval, can be obtained by
HS =E W * I . , (A-3)
n 3=0 J n-j
where I is the incident solar radiation into the shade assembly including the reflection
from glSss as shown in figure 5 per unit window area.
494
INDUCTIVE
DESIGN PROCESS
DEDUCTIVE
DESIGN PROCESS
N > I
DECISION
DERIVE EFFECTSn^
CHECK CONFUCTS
CHANGE
DECISION
N ■ N ♦!
YES
CHANGE
I DEA
REQUIREMENTS
CRITERIA
IDEA
OBJECT
DESIGN
(Ho
OPTIMUM
RANGE OF
► BJECT
«= SELECTION
Figure 1 Two basic types of design process
495
496
B , tan0, tony
1-
o|
AA
AB
= 0
= 0
Calcu
DL
late
, FL
Calcu
AS, A
late
M, VF
AA= AA + 5
or
AB= AB+5
DL, FL
AA, AB
AS, AM, VF
DL=DLx|.|
or
FL= FLxl.l
DL,FL
Figure 3 Flow chart of Phase II calculation
497
Figure Z| Plotter dravifings of example shapes of sun shade
498
499
[watt/m2]
1 [kcal/m^h]
Figure 6 Weighting factors relating the incident solar radiation into the shade
assembly to the heat discharged from the shade surfaces
500
Calculation of Smoke Movement in Buildings
T. Wakamatsu
Building Research Institute
Ministry of Construction
Hyakunin-cho 4, Shinjuku-ku
Tokyo, Japan
For the purpose of personal safety from the hazard of smoke in
building fires, it is necessary to keep escape routes clear of smoke or to
keep the smoke concentration on the routes thinner than allowable one until
the evacuation of the occupants is completed safely. For this, it is natu-
rally required to control smoke movement by some mean. There should
be a need for some design system, so called "smoke protection design
system", to plan the reasonable and effective system suitable for every
building to secure occupants from the hazard of smoke. Some calculation
to estimate smoke movement or to evaluate smoke control methods will be
indispensable to the design system.
Smoke movement is, needless to say, substantially caused by stack
and wind actions the same way as air flow in a building. The movement
is, therefore, practically under the influence of such conditions and
factors as burning severity in fire compartment, composition of vertical
shafts and other various flow paths and openings, temperatures on each
part of a building and the outside air, the air handling systems involving
the smoke tower or the pressurization method, and the outside wind.
If these data are given, calculation of smoke movement can be made using
a digital computer.
This paper presents a fundamental concept of the smoke protection
design system, computer techniques for calculating smoke movement and
computed results of sample buildings. A computer program has been for-
mulated to calculate mass rate of smoke or air flowing through each path
or opening and concentration of smoke and to evaluate methods of control-
ling smoke movement under various conditions for various buildings.
Key Words: Air, building, computer, concentration, control,
design, density, escape, evacuation, fire, flow, movement,
path, pressure, rate, shaft, smoke, stack action, wind action.
Engineer, Dr. Eng.
501
1.
Introduction
The increase in the number of high rise buildings and the tragic results of fires continuously
happened in Japan in recent years have attracted much attentions to the hazard of smoke and toxic
gases produced by fires in the buildings. As a result, various suggestions have been offered as
counter-measures against smoke hazars, such as the restriction on the use of combustible linings,
the effectivity of balconies on outside wall for escape, the necessity of smoke tower or the pressur-
ization of escape routes as measures to control smoke movement and so on. These are surely
available for personal safety from smoke in its own ways, however it should not be easy in practice
to apply all of them in a building. To evaluate these measures, and to solve the problem how ration-
ally and effectively to protect occupants against smoke, it will be the most important and necessary
approach to establish a design system enable to evaluate various measures mentioned above, by means
of estimating smoke movement or concentrations in escape routes and the time required to evacuate
the occupants. Since the calculation to estimate the time for the evacuation is now enabled to apply
practically (1), the only remained difficult problem to be solved is how to assume the conditions and
to calculate smoke movement under the conditions.
If a building has a perfect security to prevent an outbreak of fire, with all incombustible linings
and furnitures or some complete set of fire extinguishers as sprinklers, the building should evidently
need no further measure against fire or smoke. However, actually it is almost impossible to expect
to be that way. Therefore, the most important problem is how to make occupants escape safely in
fire by some measure, and then how reasonably and effectively to provide and plan the measures or
the facilities. The system to solve this problem is, so to speak, the smoke protection design system.
Fig. 1 shows a flow chart illustrating a concept of the design system. When the conditions and
factors of a building are given or determined, one can estimate whether the occupants will be safe
or not in fire, and one can take measures to meet the situation or consider how to plan facilities
against smoke per the procedure shown in Fig. 1. The smoke concentration "Cs ( t ) " can be estimated
for each part of the building as a function of the time "t" after outbreak of fire by the calculation of
smoke concentration or mass rates of smoke and air flowing through each opening. The smoke load to
each compartment is given as the product of the mass rate by the concentration of smoke flowing into
the compertment. The original concentration of smoke in a compartment in fire (3) can be assumed
from the combustibles and the temperature in the compartment (4). The evacuation time for the design
"Td" is given as a product of the minimum time required to evacuate the occupants "Tm" by a safety
coefficient " e " as Td = £ Tm. Tm can be calculated for each escape route based on width and length of
escape routes and its number in quantity, type and quantity of fire alarm system, lighting and guiding
sign, constitution of the occupants, and human psychology in emergency. The allowable smoke con-
centration "Cs/^" may be given from the visible distance required for the occupants to escape (5).
According to the procedure shown in the Fig. 1, we can predict from the values of Cs(t), Td and CsA,
whether the occupants will be safe or not in fire, or whether Cs(Td) Cs^. When
Cs(Td)> Cs^, it indicates need for some further consideration to reduce Cs{Td).
Smoke is probably not so much different from air in the nature such as the density (10), the
viscosity and so on. To understand smoke movement in buildings, therefore, it is necessary to solve
the problem of how much air flows through each component and how much smoke is contained in the air.
2.
Smoke Protection Design System
3.
Analysis of Air Flow in Building
3. 1 Basic Pattern of Flow through a Path
In general, the mass rate of air through a path Q can be represented as.
502
Q = ±\/ j z^P I / R , or Z^P=R.Q2
where R: flow resistance of a path,
P: pressure difference across a path.
When two spaces adjoining each another with different temperatures, there is pressure distribu-
tion on the separation attributed to the density difference of the air. In the case of Fig. 2(a), where
the neutral plane exists between the levels of the top and the bottom of the opening, each mass rate
Ql and Q2 of air flows through the upper or the lower part of the opening can be thought as,
Qi= ±\/ I ^Pai I /Ri . or Q2= ±\/\Z\Pa2 l/Rj
where ^Pai= 4Z\Pi/9 , Z\Pa2= 4Z\P2 /9 , Ri= 1 /( 2gri ( aAi)^ ) , R2 = l/( 2 gTz ( aAa)^)
g: acceleration of gravity, : density of air, GA: effective area of flow path,
/^P;[ , Z\P2 : pressure difference at the level of the top or the bottom of the opening.
In the case of Fig. 2(b), where the air flow is one-way, the rate Q can be given as,
Q = ±\/ \Z\Pa |/R where R = l/( 2g r 2K ( QA )^ ) ,
^^=1^^+ (l + n)(; + n+2^)^ ■ "^^'Z*^^
^Pa.: pressure difference between two spaces at the center of the opening.
3.2 Wind Action
Wind pressure on a outside wall Pw is determined by wind velocity v and wind pressure coef-
ficient C which depends on directions of wind and a wall face, that is Pw = C?'v2/2g. If the velocity
profile, surrounding conditions and the nature of wind are neglected, the wind pressure coefficient C
is given by an angle Aww between wind direction and the normal to a wall face as follows (9),
C = 0. 75 when 0°^|Aww|<30° , C = -0. 021Aww + 1. 38 when 30 °<|Av/w|<;90 ° , C = -0.5 when
|Aww|>90°.
3. 3 Computer Technique for Flow Analysis
a. Basic Model and Computer Technique
Pressure in each part of a building and air flow rate through each opening or path can be obtained
by means of solving an air flow network composed of flow resistances of openings and such motive
forces as wind pressures and air gravities. There are two methods, so to speak, "loop method" and
"knot method", as computer techniques to solve these kinds of networks. Two basic patterns of the
network simulating the electric circuit are illustrated in Fig. 3 and 4, relating to the both methods.
The loop method is to solve, based on the 1st and 2nd lows of Kirchhoff, the equation of the
through quantity on the knot ^ Q = 0 and the equation of the across quantity on the loop of the network
J/^P = 0. This method has already been described in (2), but the simplest model is shown in Fig. 3.
The knot method is to solve the network with the mass rate balance for each knot or the equation
of the through quantity 2' Q = 0, as shown in Fig. 4 where a basic model of the network is shown for this
method. In this method, pressures on all knots are assumed at first, then they are corrected iter-
atively until mass rate balances of all knots are satisfied. In Fig. 4, when static pressures p-^~ P4 arc
given, the pressure P to be solve is obtained as a root of the following equation;
£Q= I±s/ \Pi-Ei - P\ /Ri = 0
The flow chart shown in Fig. 5 illustrates an iteration procedure for correcting unbalanced mass
503
rates in the above equation.
b. Network for Practical Building
Fig. 6 shows practical patterns of the network of air flow in buildings. A computer program was
formulated using the iterative technique shown in Fig. 5, to solve the network composed of the patterns
shown in Fig. 6, by which it is enabled to calculate air and smoke flows under various conditions on
various building. Fig. 7 shows a network of an actual building in Tokyo, as a simple example. The
results for this building, calculated by the loop method, has already been published (2), but a part of
them is shown afterwards.
4. Smoke Spread and Smoke Concentration
To estimate the safety of occupants in escape routes, one must calculate the rising rate of smoke
concentration in each escape route. So it is necessary to obtain the time in which smoke appears at
each escape route and to calculate smoke concentration after smoke reaches there. As a whole, it is
very difficult to grasp the smoke movement in inicial stage of a fire, because temperature of smoke
is transient and under unsteady state. So, calculations was made based on the following assumptions;
(1) temperature in each part is constant during fire,
(2) smoke diffuses uniformly itself all over the space instantaneously except in vertical shafts
and the corridor of the floor on fire.
4. 1 Smoke Movement in Corridor of Floor on Fire
The nature of smoke, particularly its temperature, in the corridor of the floor on fire is very
important for calculations of spread and diffusion of smoke to other floors. Layers of smoke and air
are generally formed in the corridor, as shown in Fig. 8, the one of smoke flowing on upper part of the
corridor from burning compartment, and the other of air flowing on the lower part to the compartment.
The temperature of the smoke layer varies according mainly to the distance from the opening of
burning compartment and the temperature of burning compartment which varies not so much after the
flash-over. Since the temperature as a function of the distance and the time after breaking out of
fire is difficult to solve and not so much usable for the purpose of these calculations, one may assume
it as constant for the time, and then regard it as a function of the distance. Fig. 8 shows a cross
section of a smoke layer of thickness H and width W (equal to the width of corridor). Assuming that
heat transfer coefficient to the surroundings h, the specific heat of smoke at constant pressure Cp
and the temperature of the air Q^^ are constant, a heat balance is shown by the following equation
(1) on the crosshatched finite slice of thickness dx and distance x from the opening of the burning
compartment.
dd
- Q • Cp-( g,^ ) • dx-dt - 2h(H+W) ( e-(9o) ( 1-/?) dx dt = HWrCpdxZX^ (1)
where Q is mass rate of smoke in its layer, d is the temperature of the slice or smoke x distant
from the opening, z\0 is the varied temperature of the slice after the elapse of a finite time increment
dt, and ^ = (^dsx — do ) / { 6— do) where ^ sx is the temperature on the surfaces of the surroundings at
the position x from the opening.
Assuming the temperature to be constant or = 0, Eq. (1) becomes
dd _ 2h ( H+W) (!-/$') r ft_ ^ )
dx Q Cp I. 0 ;
504
Therefore, 0 is given as
d=do+(dF-do) exp (-a0x)
2 ( H+ W)
where
(2)
a =
Q Cp
X - c ■ fl
h'exp(h2t/^ cp) erfc h s/t/Jcp
temperature of smoke in burning compartment
the time representing the elapse of fire
heat conductivity, specific heat and density of the materials of surrounding walls of the
corridor respectively
In Eq.(2), 0 can be obtained by assuming that the surroundings of the corridor are made of semi-
infinite solid. Fig. 9 shows a graph of ®vs. t/^c/5 for the values 40 120 of h(Kcal /m^hr °C).
One may use 0 at an average time like the half of the evacuation time based on the assumption of
steady state.
Assuming that t = 0 or |-;eneration
air flows in
building
safety coef-
ficient; £,
smoke load
:-.;::0ke corjcen-'
tration in
escape route;
MO ,
minimum time
for evacuation
to escape; Tm
evacuation
time for
design; Td
Td = e Tm
allowable
smoke con-
centration;
CsA
olan to make occupants escape safely (■
s(Tq;
Fig.l Flow Chart of Smoke Protection Design System
A,
Oi
(rBhO
' B
(a)
Fig. 2 Basic Pattern of Plow Through Opening
509
Pl.'iniclally assumed ptessure
ho - inicial increment ( CONStanK ■<-))
Q ; total of mass
flow in a SI
Q,= Gf(P,)|
yes
I h= -^hc I I h = K I
P==(P,Q2-PA)/(a -Q,
Q^^Qr (P)
P2 =
P
Q
2jJ-~-
■ no
P,= P2
, P2= P
, Q2= Q
SOLUTION
Pig. 5 Flow Chart of Interation Procedure for
Correcting Ujibalanced Mass Flow in a Space
-f EW
-^Pb)T T
(b) Detail of Net Work on Burning Room and Burning Floor
marks :
0 : Outside air
R ; Room(compartment )
Rb: Burning room
C : ODrridor
L ; Lobby
(a) Net work of a Floor
S: Stair
Ew.Wind pressure
VD : HVAC duct
ST : Smoke tower
RD: Return duct at corridor
AS: Air suply duct to lobby
or stair for pressurizntion
SP; Air suply duct or ver-
tical shot
Fig. 6 Net Work Shows a Pattern of Air Flow Paths
under Wind and Stack Action
510
air Wb ""idx^
opening of burning room
smoke
air
Fig. 8 Smoke on Corridor of Fire Floor
511
Fig. 9 Heat Loss Factor on Surrounding Surface
^ T.Vi
h; Qi.
I ^' tCi
i-l Fl. Ci-l
A : cross section area
H: -floor height
(a) Qi>0
( b) Qi ^ 0
Vi - (Qi-1- Qi)
Ci = C i -1
Vi =
(Qi-1^ Qi)
3- A
P _ Ci-lQi-l*C'iQi
^' Qi-uQi
Fig. 10 Smoke Flow in Vertical Shaft
512
COMPARTMENT
(OFFICE ROOM )
TSP/MR q»SE )
PLAN OF A BUILDING
EFFECTIVEWIDTH OF CRACK
olA - A - 0 00 3 ( m )
SCALE UNIT ; m
PARE GLASS
VENTILATION OPENING ; 52 ( PER FLOOR)
VENTILATION OPENING
(AT BOTTOM OF WINDOW )
Fig. 11 Plan and Opening of Example Building (Example-l)
Fig. 12
I 2 3 4 5 6 7 a 9 10 II 12 13 14 15 16 17 IB 19 20
Volume of Supplied Air ( kg /sec)
D 1 ""2 ^2 "4 '1
Time ot Air Change ( I /h )
Relationship between safety time for escape and
volume of supplied air or times of air changes
in staircase
\30*
Wind (velocity : 5m/s SSE 30°)
marks :
RM
DS
RD
ST
A5
room
HVAC duct space
return duct
smoke tower
air supply duct
door's shut in fire
opening •.
wmdovv/ on burning RM; 2''2(m)
exhaust opening on ST ; 1.5 »l
door of lobby on fire, 2*2
Fig. 13 Plan of tixample Building (Example - l)
513
out sfde
0.15
window
6.77
14. OA
Qvent.op. []
(N)
burninq rm. '
0.8
2 22 opening ; (m)
u
corridor
♦•8.37
4.83
□
window -.2x2 Q
vent, op ;0.3»1 12 13
door ; 2«2 ^
transom
window;1»2
1.76
7.46
Fig, I'll Mass Rates (kg/s) of Smoke and Air of Burning Room
burning rm.
RM-
RM
15.7(3^
^5.5(2.K)
(D
,07(0)
RM0I
0,6 (0)i
2.5(0)
192 75
(3) (2.2)
20.5(3)
— 75 (2.2)
1.3 (3)
( 2.K)
(ES)
25(0)
|l.2(2K)
r — • air supply
-►3.6(3)
- 2.0(2.7)^
2.0 (2.65) (ii)
O.A ( 0 ) ^
SD
RM ; room
ES . elevator shaft
Ll.in lobby 1,11
SI.SH : stair case 1 ,11
ST . smoke tw/er
755(2.1 )
STi-^
1.2(1.8)
.9(0)
in.
7.A (2K)
77(2.0)
027(0 )
4 RM (T)
0.27(0T ^
Fig, 15 Smoke Flow on Corridor of Fire Floor
outside
m1.97 ^ .
)
zio
i02S)
151 ^
7A0
(035)
VAl
9.15
s(0.35)
1.29
1.2 35
-(035)
1.17
1 3.77
(035)
1.03 ^
^
,(0.A1)
086 y
12.76
(0.A1)
0.66^
836
(0.62)
0.36 ^
^70A
0=1
OA 3
air supply
duct
-338
corridor outside air supply
.OA 5/^ 159 <^'^ct
-1.61
3.35
5.22
652
I 1 1-23^
t
2.0A
.(0.15)
1A9
-3. AO
-^729
(0.1 5)
1.38
' 895
(01 5)
1.26
-1,62
"^12.09
(0.15)
1.1 A
"^^AO
(015)
0,99^
3.31
11,2A
(0.1 9>)
0.82^
-^121 A
(0.1 8)
0^^
5.21
' 73 A
(030)
^ 737
JO. 15)
0 55^
6,50
(a) Elevator shaft, (b) Stair easel
I I time in which smoke head arrives at each
( ) smoke concentration ,( optical) , ( 1/m )
other figures : mass rate of smoke or air ( kg/sec
( c ) Stair case II
floor level, ( sec.)
Pig, 16 Smoke Flow in Vertical Shaft
514
Winter
IT)
CLOSE
in
o
CD
0
1
0
cn
b
1
-0.8
b
OO
b
b
cn
b
<^
0
-3.0
-2.9
t-7
7*
0
fs
cn
cn
0.10
if)
1
1
o-s
cn
si
CD
si
u>
si
32.2|
o
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u>
0
0
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in
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7
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cn
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cn
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1
1
si
CO
CO
2I.1I
o
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1
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0
1
cn
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1
vj-
0
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vj
0
0
«p
0
«J
0
CD
b
m
1
CM
si
0
1
cn
0
cn
CM
CO
0.02
1
1
0
0
sT
0
in
0
ID
0
0
sT
1
cn
0
1
1
IP
c~
00
0
CO
0
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1
in
1
\
0
si
CO
0-13
1
1
cn
p
20.8 1
Sunnnner
in
CLOSE
ID
o
OO
0
u>
0
U>
0
0
0
IX>
0
u>
0
10
0
10
0
0
CM
0
CM
0
1
0
1
0
I
"cn
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cn
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cn
0.10
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Kf)
1
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sj
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si
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ui
25.7|
o
caD
0
0
0
0
0
0
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1
-0.3
cp
tn
0
03
0
0
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0
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f
tn
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1
0
I
0.1 1
CM
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in
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517
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518
Use of Actual Observed Solar Radiation
Values in the Determination of
Building Energy Requirements
John C. Thies, P.eJ
Southern Services, Inc.
Birmingham, Alabama
The effect of solar radiation is one of the many items that must be considered
to properly determine a building's energy requirements for heating and cooling. The
intensity of direct and diffuse solar radiation impinging upon a building's surfaces
depends upon many factors; the season, locality, time of day and various types of
sky contamination.
Numerous computer programs to determine the total annual energy consumption of
buildings for heating, cooling and other uses have been written by various companies
and organizations. Different approaches are used in these programs to estimate the
effect of solar radiation on a building's heat loss or heat gain which in turn affect
the energy requirements of the heating and cooling systems being evaluated.
This paper describes a practical, rather than theoretical, approach for estimat-
ing the effect of solar radiation on a building's heat loss or heat gain. The ap-
proach described is incorporated in a computer program that calculates a building's
total annual energy requirements on an hourly basis. Basically, available solar ra-
diation data as observed on a horizontal plate at several locations in the Southeast-
ern United States over a period of years are converted to solar intensity values nor-
mal to the sun's rays for each hour of a year. The advantages and disadvantages
over the theoretical approach are discussed.
Key Words: Solar radiation, actual radiation, observed radiation, actual ob-
served radiation, building energy requirements, heating and cooling requirements.
1. Introduction
Consulting engineers and utility personnel often are required to estimate the annual heating, cool-
ing and electrical energy requirements and energy cost of different buildings. Such estimates can be
much more difficult and time consuming to calculate than the design point heat loss or heat gain for siz-
ing the building's heating and cooling equipment. Calculation of the annual energy requirements involves
a summation of the combined effect of many factors over a lengthy time period, and these factors may vary
considerably with time.[l]2 Though the electrical requirements of a building are affected only by the
building's mode of operation, the heating and cooling requirements are affected by five factors:
(1) building location, (2) building construction, (3) building mode of operation, (4) building thermal
load and (5) weather at the location.
2. Complexity of Problem
Because of the complex and interrelated nature of the factors involved, no simple and quick, non-
computerized method has to my knowledge yet been developed for very accurately estimating the energy re-
quirements of various types of buildings; however, there are many- different analysis methods in use to-
day that provide reasonably accurate estimates of this nature. Use of past operating records on a par-
ticular building, when these are available, may provide a reasonably accurate prediction of future energy
requirements for a building being designed - provided that the factors affecting its energy requirements
are almost identical in every respect. Unfortunately, many new buildings will differ from those existing
in not just one, but in many ways. The use of averages of operating records available from similar, yet
Supervisor of Technical Services, Rate Department
"Figures in brackets indicate the literature reference at the end of this paper."
519
not identical, buildings can be misleading. There is no "average" building.
3. Digital Computer Offers Means
The most direct and reliable estimating procedure for determining a building's annual energy require-
ments to provide its heating, cooling and electrical needs is an hourly integration of the simultaneous
calculated loads of each item involved as a function of the weather and use schedules. The modern digit-
al computer offers the means for handling the vast amounts of data and calculations associated with pre-
paring such an estimate. Development of computer techniques together with improvements in the availabili-
ty of the basic data needed for the calculations are making it possible to determine the annual energy
requirements with a high degree of accuracy. Numerous computer programs and methodologies have been
written in recent years by various companies and organizations to perform this type of work. Different
approaches are used in the programs to estimate the effect of solar radiation.
4. Solar Radiation a Major Factor
The amount of solar radiation impinging on the exterior surfaces of a building has a significant ef-
fect on its heating and cooling requirements. In many buildings as a result of a particular orientation
and construction, solar radiation can have a very decided effect on the heating and cooling requirements.
Due to the numerous factors that affect the total amount of solar radiation finally reaching the earth's
surface, the exact magnitude impinging on the exterior surfaces of the building can be difficult to pre-
dict.
The intensity of direct solar radiation on a surface normal to the sun's rays above the earth's at-
mosphere is generally assumed to be approximately 445 btu/hour/square foot. In passing through the
earth's atmosphere, the sun's radiation becomes scattered and absorbed to varying degrees by water vapor,
dust, ozone and gas molecules that are present. Thus, what was only direct radiation now becomes both
direct and diffuse. The amount of total solar radiation reaching a particular surface is the sum of the
direct solar radiation, the diffuse sky radiation and the solar radiation reflected from surrounding sur-
faces. Its magnitude at any given time is determined by the moisture, the amount of smoke and dust in
the air, the type and thickness of cloud cover, the locality, time of year and time of day [2].
5. One Way to Calculate Solar Radiation
It is recognized that some of the approaches used in existing computer programs and methodologies
are a result of insufficient solar radiation data being available for the entire United States at the
time the program was written. In other instances, the approaches used were probably thought to be, and
may be, reasonably accurate. One of the more prevalent approaches has been to calculate assumed hourly
solar radiation values for cloudless days and to apply available percentage cloud cover hourly data in an
attempt to compensate for the effect of cloud cover on radiation. With this procedure, values of solar
azimuth and solar altitude angles are input in table form on a one set of hourly values per month basis.
Values for cloudless days of direct solar radiation received at normal incidence at the earth's surface
and values of diffuse or sky solar radiation assumed to be received by variously oriented surfaces for
clear or industrial atmospheres are also input for the varying solar altitudes. The program then inter-
polates the data to determine the hourly location of the sun and to estimate the hourly values of radia-
tion impinging on the various building surfaces.
6. Use of Observed Solar Radiation Values
Another approach that can be utilized to calculate the hourly effect of solar radiation on a build-
ing's heating and cooling energy requirements is to use actual observed radiation data on a horizontal
plate as an integral part of the program. This is the approach that was utilized in a computer program
developed several years ago for the group of electric utility companies in the Southeast with which I am
affiliated. The program was developed by the Mechanical Engineering Department of the University of Flor-
ida on a research contact with Southern Services, Inc. It considers the various factors mentioned earlier
and performs an hour-by-hour synthesis of a building's heating, cooling and electrical requirements on a
multi-zone basis, up to a maximum of 24-zones. After the hourly requirements are calculated, the program
simulates the performance of specific equipment to meet these requirements and determines the total month-
ly and annual energy consumptions and demands. From these values, the monthly electric, fossil fuel and/
or steam bills can be calculated.
This computer program was developed on the basis of having the capability to be used on any type of
building. Its development was predicated on being able to obtain the most accurate answer that present
scientific knowledge and available information would permit, using basic equations. In keeping with this
basis, it was concluded that the use of actual observed hourly solar radiation data on a horizontal plate
for energy calculation purposes would be preferable to calculating assumed hourly values and adjusting
them by the application of cloud cover factors. The actual observed horizontal plate values would already
520
include the effect of the type and thickness of cloud cover and the moisture, smoke and dust content of
the air. Use of these values would also eliminate any error due to an improper cloud cover percentage
being estimated by the observer. It was recognized that the effect of an industrial atmosphere would
still need to be considered.
7. Details on Use of Observed Radiation Values
Research efforts located eleven year averages of actual observed hourly solar radiation data on a
horizontal plate for various cities. This data was developed through a joint effort by the Boeing Com-
pany and the U. S. Weather Bureau [3]. Data was extracted from the report for the southeastern cities of
Apalachi col a , Florida, Lake Charles, Louisiana, and Charleston, South Carolina. (See figure number one
for a comparison of the average values of solar radiation on which this program is based and the extremes
which occurred over a 14-year period.) From the mean hourly solar radiation data in the report for these
three cities, average values in Langleys were calculated for each sunlit hour of each month. One Langley
is equal to one gram calorie per square centimeter and one gram calorie is equal to . btus. These
values were converted to btu/hour/square foot of horizontal surface. (See figure number two for curves
depicting typical hours.) Then, these values were converted to intensity normal to the sun's rays, still
in the same units. A review of these values indicated that afternoon values were somewhat excessive due
to the higher level of diffuse radiation energy existing in the afternoon hours. To obtain more realis-
tic values of direct solar radiation normal to the sun's rays in the afternoon, the morning horizontal
plate readings were subtracted from the equivalent afternoon hour's readings, with the difference consid-
ered as diffuse radiation energy. New afternoon values were then created by adding this difference to
the morning values at the same solar altitude. Equations were developed to calculate these values as well
as the sun's location for each hour of the year. (See figure number three for typical curves of the solar
radiation normal to the sun's rays as used in the program.)
8. Other Considerations
The effect of atmospheric clearness is considered by the program and the effect of an industrial at-
mosphere can be considered. An atmospheric clearness number of 0.95 is used in the equations rather than
a value of 1.00 because according to Threlkeld and Jordan [4] in the southeastern states there are rela-
tively high concentrations of atmospheric water vapor. The effect of an industrial atmosphere on direct
normal solar radiation is considered as a function of the solar altitude angle and can be varied from 0
to 100 percent. Moon's data for 40 degrees North latitude on about August 1 relating the direct normal
radiation and diffuse radiation of clear and industrial atmospheres to solar altitude is used as a basis
[5].
9. Concluding Remarks
The above comments reflect the treatment of solar radiation for hourly energy calculation purposes.
I have not discussed the procedure used for design condition energy calculation purposes. The procedure
used for these purposes is somewhat different. One may question the accuracy attained by use of eleven
year averages of hourly solar radiation data for three locations as opposed to other analysis methods.
It was concluded that an analysis procedure predicated on being able to use long-term averages of actual
observed hourly data for three locations covering The Southern Company service area was more factual and
inherently more accurate than other possible methods.
10. References
[1] ASHRAE Guide and Data Book, Applications, Chap-
ter 54, p. 645-656 ().
[2] ASHRAE Handbook of Fundamentals, Chapter 28,
p. 469-475 ().
[3] "Summary of Solar Radiation Observations", U.S.
Weather Bureau Report Number D2--1) Decem-
ber .
[4] Threlkeld, J. L., and Jordan, R. C, "Direct
Solar Radiation Available on Clear Days", ASHRAE
Transaction Number .
[5] ASHRAE Guide, Chapter 13, p. 298, Table 4 ().
521
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II YEAR AVERAGE OF
OBSERVED RADIATION . .
FOR SOUTHEASTERN U-S.A.^^^
(TYPICAL VALUES)
300 HRS.
(a) Based on Apalochicola, Fla.,
Charleston, South Carolina and
Lake Charles, Louisiana.
JAN.
APR.
JULY
MONTH
OCT.
JAN.
gure number two: 11-Year Average of Observed Radiation For Southeastern U.S.A. (Typical Values)
523
524
Design of Direct-Expansion Evaporator Coils by Digital Canputer
Donald G. Rich
Senior Engineer, Research Division
Carrier Corporation, Syracuse, New York
Jack B. Chaddock
Professor, Department of Mechanical Engineering
Duke University, Durham, North Carolina
and Consultant, Research Division
Carrier Corporation, Syracuse, New York
Heat and water vapor transfer normally occur together in the use of an evap-
orator coil for air conditioning, making the process diverse and complex. As know-
ledge of this process has developed, together with the ability to describe it
analytically, so has the need evolved for more exact procedures in practical de-
sign. This paper describes how the digital computer may be used for this purpose.
Beginning with a discussion of overall program objectives with respect to input
and output, the development of a program logic for evaporator design is described.
Decision points within the program include a logical procedure for selection of coil
dimensions and refrigerant-side circuiting. Other decision points of particular
significance are those Involving iterative procedures for arriving at designs which
match coil load conditions. Problems of convergence of these procedures are dis-
cussed. Basic equations used for performing the calculations are outlined, including
methods of determining air-side, refrigerant-side and metal thermal resistances. The
effect of variations in these resistances on overall performance is considered as re-
lated to methods of circuiting and operating conditions.
Sample solutions illustrating use of the program and output format are given.
Keywords: Air conditioning coils, coils (plate -fin) , cooling and dehumidi-
fying, computer design (digital), evaporators, heat exchangers, refrigerant
heat transfer.
1. Introduction and Objectives
The large volume production of finned-tube heat exchangers for the air conditioning and refrigera-
tion industry provides strong incentive for improving their performance and lowering their cost. The
computer program described here, as an aid to the design of direct-expansion coils, was developed to
assist design engineers in meeting these cost and performance objectives. The program should be viewed
as providing a tool for "computer-aided" design, rather than design by computer. Although many design
decisions are made automatically, key decisions, and a final choice among several alternative "good"
designs, are still required by the design engineer. Introduction of the program into actual use at the
Carrier Corporation has shown it to be of considerable assistance as a time and cost saver in identifying
that "best" design. And its acceptance, even by experienced designers, has been excellent.
Specific objectives for the development of the computer program were as follows:
1. To permit more effective use of the accumulating data on heat transfer and pressure drop for re-
frigerants evaporating inside tubes and air flow over coil surfaces.
2. To study the differences which would result from computer-aided design, using more detailed and
fundamental heat transfer relationships, as compared with existing design procedures.
3- To provide a tool which would permit the designer to arrive nearer the optimum coil configuration
for a given task.
h. To identify critical areas in which present information is not sufficiently precise to satisfactor-
ily determine an optimum design, and to plan research efforts to overcome them.
525
2 . Overall Program Logic
The design of an evaporator coll, like most design procedures, is not a straightforward process. It
is necessary to make a number of initial assumptions regarding coil configuration, air flow rates, and
refrigerant conditions. The more experienced designer will have acqiiired certain rules and judgments
which make it possible for him to choose initial values that produce a near-optimum solution. Neverthe-
less, even he will have to make a few trials and adjustments to match satisfactorily the particular con-
straints for a given system.
Our most challenging task in developing a computer-aided design procedure for evaporators was to
bring into its logic relationships which express quantitatively the judgment of experienced designers.
In addition there was the overriding goal to make the program a flexible tool in the hands of the de-
signer. While key assumptions and decisions could be made by the program, they must not be hidden frcm
the user. In fact it would be desirable for the designer to override key program logic, and to specify
particular constraints on certain variables where he desires. In general he should be able to guide the
computer calculations, when desired, to confom with his experience and judgjnent in obtaining a satis-
factory design.
2.1 What it does - general
The program determines the physical dimensions, leaving air conditions, heat transfer characteris-
tics, and manufacturing cost of a direct-expansion air cooling and dehumidifying coil. As input it re-
quires geometric data defining the type of plate-fin heat transfer surface, constants and exponents to
calculate air-side pressure drop and heat transfer performance, required cooling load, system operating
conditions, and cost data.
The procedure is to make an initial assumption with regard to air quantity (about ^00 cfm/ton for
air conditioning applications) , and air face velocity (usually between hoo to 500 fpm) and calculate the
coil dimensions. An iterative calculation then matches the heat transfer rate to the required cooling
load. The iterative procedure either adjusts the air face velocity or the coil size to match the loads
to within one-half of one percent. Finally, the program calculates the leaving air conditions, the air
pressure drop, the sensible heat factor, and the coil cost. The program also has features to automati-
cally index to another air velocity or coil size and repeat the above calculations. The designer is
thereby provided with several alternate designs to assist him in either making a final choice, or re-
specifying key conditions in a continued search for an "optimum" coil design.
2.2 What it requires
The user of the program must supply data on the plate-fin type heat exchanger surface, the system
operating conditions, and the manufacturing costs. Figure 1 is a typical input data sheet. The quanti-
ties appearing thereon are as follows:
a. Coil data
(1) Description, Refrigerant (12 or 22) , and Identification Number.
(2) Tube outside diameter and wall thickness - Dq and t^ (inches).
(3) Hairpins or return bends, and return bend inside diameter - Dj_-b (inches).
(h) Tube spacing (transverse and longitudinal) - and Pj, (inches) .
(5) Fin spacing and thickness - Nf (fins/inch) and tf (inches).
(6) Surface heat transfer constants - C-^ and n^^ (for the determination of the air-side thermal
resistance, as explained in Section 5.2).
(7) Surface pressure drop constants - and n (for the determination of the air-side frictlonal
pressure drop, as explained in Section 3.2 j.
By storing the heat transfer and pressure drop characteristics of a given type coil in a disc file,
items (6) and (7) can be replaced by an identification number which is related to the location on the disc
•where the information is stored. This number is 5 in the example given in Figure 1.
b. System operating conditions
(1) Cooling load - q(Btu/hr)
(2) Saturation temperature at suction - tyQ(°F)
526
(3) Subcooled liquid temperature at inlet
(k) Suction superheat
(5) Entering air dry-bulb temperature
(6) Entering air wet-bulb temperature
(7) Atmospheric pressure
(8) Safety factor (see Eq. l)
(9) Minimum air face velocity
(10) Air face velocity increment
(11) Maximum air face velocity
c. Cost data
The cost of materials for construction of the coil core can be expressed as the sum of the costs for
the tubing, the fin material, and the return bends. The tube and fin costs will depend on the weight or
volixme of material used. The total material cost is then written as
Cm = ^t ^t ^ Cf Vf ^ % \
The input data then requires
(1) Cost of tube material - C^ ($/cu in)
(2) Cost of fin material - C^ (t/cu in)
(3) Cost of return bends - C^ (t/bend)
More detailed cost calculations would bring into consideration costs of the refrigerant distributor
and feeder tubes, solder, labor, etc.
2.3 Decision Points
A first and major decision is where to start the design calculation. Other key decisions involve
the refrigerant circuiting of the coil, and how to direct the search to insure a final design choice
which is a near optimum one. The program logic which makes these decisions originally evolved from the
judgment of experienced designers, and underwent refinements as it was put to use on a variety of evapor-
ator designs.
a. Initializing coil dimensions
Three choices are possible as follows:
(1) Case 1 - Aspect ratio
Under this case, the ratio of coil length between tube sheets to coil height (aspect ratio) is
specified by the designer. In iterating to arrive at the design cooling load the length between tube
sheets is varied, hence the final design does not correspond to the exact value of aspect ratio.
(2) Case 2 - length between tube sheets
With this selection the program iterates on air face velocity so that the final design does conform
to the specified length dimension.
(5) Case 3 - Number of tubes in the coil face
This is equivalent to the selection of the face height of the coil. With this design constraint the
program holds the given height and iterates on the length between tube sheets to match the design load.
If the user does not choose to select any of the above, the program sets the aspect ratio at a value
of 2, and proceeds as in Case 1.
- tsub(°F)
- Atsup(°F)
- *ai(db)(°F)
- tax(wb)(°F)
- Patm^'"-
- Fs
- V__, . X (ft/min)
70(min) ' '
- AV^o( ft/min)
- V_„, X (ft/min)
T^o(max) '
b. Air velocities
Air face velocities for DX evaporator coils have
coil size which may not be economically competitive.
and flow rates
a restricted range. Low velocities require large
High velocities may cause entrainment of condensed
527
water on the coil surface, and carry over into the discharge air stream. As listed above for the system
operating conditions - input data, the user must specify a minimum, maximum, and incremental air face
velocity. Reasonable limits are 300 fpn and 600 fpm for the minimum and maximum velocities, although
velocities outside this range may be used in special cases. The incremental air velocity, AV^^, directs
the program to index upwards from ^yo(ja^±j^) to (max) that increment. A good initial selection would
be 100 fpm. In the final search for a best design tne increment may be made smaller.
An air flow rate of hoo cfm per ton has proven to be a good choice for starting the design in air
conditioning applications. This choice usually leads to an operating sensible heat factor of between 0.7
and 0.8 for a 3 row deep coil at ^00 to 500 fpm air face velocity. In iterating to arrive at the design
cooling load, and in automatically indexing to new design configurations, the cfm/ton changes.
c. Refrigerant circuiting
If the number of circuits is not given with the input data a subroutine is called which determines
circuiting automatically. In this subroutine the number of circuits is selected so that the refrigerant
flow rate is within the range of good design practice. In addition, circuiting selections are limited
to those which will provide balanced refrigerant distribution, a factor of considerable importance to
good performance .
For an air conditioning coil with l/2 inch tubes, experience has shown that a good starting point for
determining the number of circuits is to assume a circuit load of l6,000 Btu/hr. At smaller or larger
tube diameters the loading factor of l6, 000 must be decreased or increased correspondingly. Changes in
the pressure level also affect the loading factor because of density changes of the fluid. Relationships
to account for these effects are incorporated into the program logic to calculate an initial value for the
number of circuits. The program next requires that both and the ratio N|-/Nc be integers. For example,
if = 2h tubes in the coil face, then the number of circuits, Nq, permitted is 1, 2, 3, 4, 6, 8, 12, or
2h. The selection will be the smallest of these numbers which does not exceed by more than 30 per cent
the initial value.
The above procedure insures that a balanced refrigerant circuiting arrangement will result. The
experienced designer may recognize a satisfactory circuiting arrangement not permitted by the simple
program logic. In this case he may specify in the input data, and override the computer selection
procedure .
d. Indexing to new designs
Depending upon the designer's choice of Case 1, 2, or 3 in Section (a) above, the computer is dir-
ected to iterate on either air face velocity or face length to match the design load. After the first
design has been found, provision has been made for autcmatically seeking alternate designs using the same
method of iteration. The first method of indexing to a new design is to change the number of tubes in
the coil face by first two greater and then two less than that found in the initial design.
When the design is proceeding on the basis of aspect ratio (Case 1 or no designer specification) ,
or on tubes in the face (Case 3) , the design starts with the minimum air face velocity of V^^/ . x .
After the initial design, and those at + 2 additional tubes in the face are completed, the compuier in-
dexes to a higher face velocity by the velocity increment AV^^. Again at the completion of an initial
design for this velocity the program calls for designs at + 2 additional tubes in the face. The indexing
to increasing air velocities continues according to the equation
V^o = V^o + I (^V)yo
with I = 1, 2, 3, — , until V^^ exceeds '^jo^^nax)-
In Case 2 where the length between tube sheets is specified, the procedure for indexing to + 2 tubes
in face is used, but the incremental air velocity is not. If the number of refrigerant circuits is spec-
ified, or if the face area of the coil is fixed by giving both Lp and with the input data, then no
automatic indexing occurs .
2.^ Flow Diagram for the Main Program
A condensed version of the main program flow diagram, labeled DX - 12/22, is presented as figure 2.
As used on an IBM computer it calls on nine subroutine programs, designated: R, S, T, A, B, C, D, E,
and H. Referring to circled numbers on this figure, the explanatory phrases below will assist in follow-
the program logic ,
528
(1) Subroutine program 'A' reads the input data of figure 1, and supplies index numbers to carry out
the automatic indexing to new designs, described in (d) above.
(2) Subroutine 'R' calculates refrigerant properties for either R-12 or R-22.
(3) Subroutine 'S' calculates air-side thermal resistance and pressure drop at standard air con-
ditions for the specified plate-fin siirface.
(h) Subroutine 'T' calculates the metal resistance of the finned coil by the sector method.
(5) Subroutine 'H' calculates the enthalpy of moist air at the coil inlet. The other calculations
here are to make a temperature correction to the air-side thermal resistance, and set an initial
value of air flow by the rule of hoo cftn/ton.
(6) Subroutine 'B' calculates the coil geometry, including the number of refrigerant circuits.
(7) Subroutine 'C calculates refrigerant-side heat transfer coefficients and pressure drops, the
mean temperature difference in the superheat section and the superheat length.
(8) Subroutine 'D' calculates the mean temperature difference in the evaporating section of the coil.
(9) The load calculation is made by determination of heat exchange in both the evaporating and
superheating portions of the coil.
(10) The convergence routine to match calculated to design load. (See Section h.2) .
(11) Subroutine 'E' calculates the leaving air conditions, the sensible heat factor, coil apparatus
dew point, and materials or manufacturing costs.
(12) This is the automatic indexing sequence to set up for additional designs at + 2 additional
tubes in the face, and at incrementally higher air velocities.
5. Basic Relations
The flow and heat-transfer processes occurring in a direct expansion evaporator are exceedingly
complex. On the air side heat and water vapor transfer simultaneously between the air and the fin sur-
faces. On the refrigerant side a series of changing two-phase gas-liquid flow patterns occur due to the
increasing ratio of vapor to liquid flow rate. These changing flow patterns and velocities profoundly
affect the heat-transfer coefficient and pressure gradient.
Figure 3 illustrates, in an approximate way, the heat-transfer coefficient and temperature behavior
of a refrigerant as it moves through an evaporator tube. Two sets of curves are shown, one for high
loading and the other for low loading. As shown in this figure, the heat transfer coefficient increases
to a maximum and then decreases sharply, eventually reaching a value corresponding to that for pure gas
flow in the superheat section. The increase in coefficient is due to increasing shear at the vapor-
liquid interface. The decrease is due to the development of dry areas on the wall, a condition which
occurs at vapor qualities on the order of 0.8 in typical evaporators. Experimental determination of
these variations in coefficient have been reported by Anderson, Rich and Geary (l)"''
It is clear from figure 3 that an accurate calculation of the heat transfer in an evaporator cannot
be made using a single average value of the refrigerant coefficient. Ideally, a step-by-step calculation
could be performed such that local variations in coefficient, refrigerant temperature, air enthalpy, and
surface temperature are accounted for. Such a procedure, however, would be complex and time consuming.
As a first approximation, therefore, the present program divides the coil into two sections - an evap-
oration section and a superheat section - with average coefficients determined for each. Coil capacity
is then calculated as follows:
F S At \ F S At
s o m \ s o m
R + R / R + R
r m / r m ,
evap ' sup
(1)
where Sq = external surface area (prime plus finned)
Atjjj = mean temperature difference between the refrigerant and the wetted coil surface
R^ = thermal resistance to heat transfer between the refrigerant and the inside surface
of the tube wall per unit of external surface area
Rjjj = thermal resistance of the fin and tube material per unit of external surface area
Fg = a safety factor specified by the designer
Procedures used for calculating At , R and R are described in the following sections.
m-" r m
■""Figures in brackets indicate the literature references at the end of this paper.
529
5.1 Mean Temperature Differences - Surface Temperatures
Figure h presents two examples of circuiting arrangements which might be used in direct-expansion
evaporator coils. In kk (labeled thermal parallel flow) the refrigerant enters at the coil leaving air
face, flows through the coil generally counter to the air flow, and discharges at the entering air face.
In (labeled thermal counterflow) the refrigerant enters at the entering air face, flows through the
coil generally parallel to the air flow, but returns to the face for the final pass (tube marked S) . Both
of these arrangements have the advantage of providing superheating in the region where the air temperature
is maximum. The second arrangement has the additional advantage of providing an approximate thermal
counterflow relationship between the air and refrigerant. Although other arrangements may be used in
practice, depending upon economic considerations related to the application, those shown in figure 2 are
sufficiently typical to be useful as models.
Figure 5 is a simplified thermal diagram for an evaporator depleting the evaporation and superheat
sections and defining the various terminal temperatures and enthalpies used to calculate the mean temper-
ature differences. Circuiting is the thermal counterflow type as shown In figure ^B, with superheating
assumed to occur in tubes at the coll face. In figure 5 this results in a discontinuity for the plot of
air enthalpy (h^^) and coil surface temperature (t ) vs circuit length. As Illustrated the superheat tube
section is in contact with entering air (h^^ = hg^^J.
Using temperature symbols as identified in figure 5, the following equations can be written for the
mean temperature differences:
Evaporation Section
' *si - V \
log
\ *S2 - *r2 1
thermal parallel flow
(t - t ) - (t - t J
si rs S2 ri
or At = ~ r (5)
m / t , - t '
log
(4^)
^ S2 ri /
Superheat Section
(t - t ^) - (t - t J
'm
thermal counter flow
At =— ^ (h)
log
(t - t \
S3 rg \
t - t I
S4 ra /
Referring to figure 5, note that tpo is the temperature at saturation corresponding to the refriger-
ant pressure at the coll outlet. This value Is an input to the program, as is the superheat, tj.^ - t^^^.
The other refrigerant temperatures are direct functions of the tube-side pressure drop; t-^^ - tj,Q is the
temperature drop due to pressure drop in the superheat section and t^x - t-^^ is the temperature drop due
to pressure drop in the evaporation section.
The coll surface temperatures will depend upon the air flow conditions, the refrigerant conditions
and whether the surface is wet or dry. The computer program presented here assumes that the coll surface
will be completely wetted. This is not a serious limitation for a design program since evaporator coils
normally operate fully wetted at normal design conditions. With this assumption, each of the surface
temperatures can be related to a coll characteristic, C, by the equation(2)
where t^ = surface temperature
tj, = refrigerant temperature
hg^ = air enthalpy
t^ - t R + R
s r m r
h - h^ c R
as pa
= C (5)
530
hg = air enthalpy- at saturation at tg
Cp = humid specific heat 0.2h'^ Btu/lb(ia
Ra = thermal resistance between the air and surface per unit of external surface area
For the evaporation section of the coil circuit a single value of the coil characteristic is used,
based on an average value of the refrigerant-side thermal resistance. Values of tg-,^ and tgg are then de-
termined from eq (5) using hai - and hg^^ and, respectively, tr^^ and t^^ ^rs ^"^^ ''^ri themal par-
allel flow) .
For the superheat section of the coil circuit two values of the characteristic are used. At the en-
trance the surface temperature (tgg) is based on the evaporating coefficient and t^.^; at the exit the sur-
face temperature (tg 4) is based on the superheat coefficient and t^.^. The entering air enthalpy, hai> is
used in both cases reflecting the assumption that the superheating tube passes are located on the enter-
ing-air side of the coil.
A computer procedure for solving eq (5) is given in Section h.l.
3.2 Air-Side Thermal Resistance
Because of the many geometric variables involved, the air-side thermal resistance for plate-fin coils
is determined by experiment. Fin spacing and thickness, tube spacing and diameter, number of tube rows
and fin surface configuration are variables upon which the coefficient depends. Generalized relationships
which can predict the effect of these variables are lacking. Detailed procedures for experimentally de-
termining the air-side thermal resistance of cooling and dehumidifylng coils are given in ASHRAE Standard
55-6^ (3).
For the small temperature differences and limited velocity range encountered in normal air condition-
ing and refrigeration applications, convectlve heat transfer data can be represented accurately by the
Nusselt equation.
- f-^f' - (6)
k ^ \ \x I r
Setting m = 0.*+, eq (6) can be solved for R^ (= l/h) , to give
^a - \~K
k P •
r
where cp^is a properties function to account for variations from standard air conditions.
An approximate equation for q5^, normalized to standard air conditions of 70° F and 1 atmosphere, is
^1 " 1 + 0. (1.109 + n^) (t - 70)
Equation (8) is accurate within + 1 per cent from -25°F to 175°F.
The frictlonal pressure drop can be calculated in a similar manner. Thus
Ap =
2P gp
2 g^ D
1 + m
m \ 2-m
G
or Ap
C cp V 2
2 ^2 70
(9)
531
where qs^ accounts for variations from standard air conditions.
C-^, n^, Cg and n are empirical constants fitted to the experimental data for a particular geometric
coil configuration. A file of these constants for a variety of coil types can be stored for automatic
access by the computer. Alternately, the designer can supply values to be read as part of the input data.
5.3 Metal Thermal Resistance
The metal thermal resistance is the sum of the resistance of the fins and the resistance of the tube
wall. The following equation relating the metal resistance, B^, to the fin efficiency f), is taken from
Reference 2.
R c
a p
D. S /S.
1 o' 1
2 k,
log
D.
1
(10)
Herein, h^ = dhg/dtg; k^ is the tube conductivity; Dq and Ti^ are the tube OD and ID; and , Sf,
and Sj^ are the external prime, external finned, total external, and internal surface areas respectively.
Various methods have been proposed for calculating the fin efficiency. Where the fin shape associ-
ated with each tube is nearly square the efficiency of an annular fin of equal area can be used {h) .
Otherwise, more accurate results can be obtained using the sector method (h) (5). The present program
utilizes a subprogram based on the sector method.
3-^ Refrigerant-side Thermal Resistance and Pressure Drop
Experimental measurements of evaporating heat transfer coefficients in tubes have been reported in
the literature, and several methods of correlating these data have been proposed. Reference 6 contains
a summary of experimental results and correlating equations which are applicable to forced convection
evaporation of refrigerants. None are completely satisfactory for the complete range of conditions en-
countered in evaporators. As stated in Reference 6, "the single equation which can be recommended for
broadest application to refrigerant evaporation in tubes is that of Pierre (7) • Altman, Norrls and
Staub (8), and Chaddock (9), have fitted it to a wide range of Refrigerant 12 and 22 data."
Pierre's equation for exit qualities < 90 per cent is
Nu = 0. (Rg^Kj.)°"^
or h^ = 0.
G D.
H
J Ax h
fg
(11)
where Ax
L
D.
1
J
change In vapor fraction
tube length
tube inside diameter
liquid thermal conductivity
liquid viscosity
latent heat
mechanical equivalent of heat (778 ft-lb/Btu)
unity.
In the present program a modified form of Eq. (ll) was used In order to cover vapor fractions up to
The heat-transfer coefficient for the superheat section can be calculated by the well -known methods
for single-phase forced convection in tubes. McAdams (lO) , after critically evaluating a large amount of
data covering a wide range of conditions, gives three equations. One of these Is called the Dittus-
Boelter equation, and is expressed as:
532
h D.
1
,023
D. G'
1
0.8
0.4
Pr
or h = cp^
(02)
1
where cp^ is a function of the fluid properties.
Reference 6 tabulates values of cpg as a function of temperature for various refrigerants. The
following simple polynomial expressions can be used to calculate cpg with a maxim\im error of 0.7 per cent
over the temperature range 0 to l6o°F.
R-32 vapor cpg = I.816 x 10"® + 3.2lk x 10"® t + I.786 x 10"^ t^
R-22 vapor cps = 1.97^ x 10"® + 3-039 x 10"® t + I.II6 x 10"^ t^
The pressure drop in a direct-expansion evaporator has several components. These include pressure
drop across the bends, pressure drop due to friction in the tubes, pressure drop within the suction
header, inlet and exit losses, and a pressure drop due to acceleration of the refrigerant as it flows
through the coil. In the present program header losses are not included (pressure at the exit of the
tubes has been chosen as a program input), and inlet and exit losses have been neglected. Of the re-
maining losses (bends, friction and acceleration) the acceleration loss is generally smallest and friction
largest, although bend losses can predominate in very narrow coils.
Several methods have been proposed for calculating friction pressure drop for two-phase flow inside
tubes. The one proposed by lyfertinelli and coworkers (ll), (12) has received widest acceptance because of
its general applicability. A somewhat simpler method is that based on the friction-factor equation. It
has proven to be satisfactory in correlating data for restricted ranges of conditions.
The basic form of the friction-factor equation is:
= — f ^ (13)
2 p i
where L is the total circuit length and G is the refrigerant mass velocity based on the total flow rate
(liquid plus vapor). Various definitions of the two-phase friction factor, f, and two-phase density, p,
have been proposed. Pierre (13) uses an average between the liquid and vapor densities, and defines his
friction factor in terms of Kf/Rg (see eq n) . A similar approach was taken in the present program ex-
cept the vapor density was used and the effects of inlet vapor mass fraction were incorporated in the
friction factor.
In addition to the pressure drop due to friction there is also a loss in pressure to accommodate the
acceleration of the refrigerant as it changes frcm a liquid to a vapor. The acceleration pressure drop
can be calculated by the relation proposed by Martinelli and Nelson (12) . For complete evaporation this
relation is
^2 r (1 - X )2 X 2
where R^ is the fraction of the tube filled with liquid at the inlet.
The following polynomial expression, based on the curve given in Reference (ll) , can be used to
calculate R^
L
log^Q \ = " O.Shhl^ + o.ii555V - 0. + 0.
533
Virtually no data is available in the literature for pressure drop of refrigerants in bends. As an
approximation, therefore, the pressure drop for the bends is calculated in the same manner as a straight
tube, using a length equal to 75 diameters. This practice is commonly used for single-phase flow (lO) .
3-5 Leaving Dry Bulb Temperature, Sensible Heat Factor and Coil Costs
After the program calculations have converged to a coil design whose capacity matches the given load,
a final subroutine is called which calculates the leaving dry-bulb temperature, the sensible heat factor,
and an estimated cost.
Using the relationships recommended in Reference 2, the leaving dry bulb temperature is calculated
by first determining the saturated air enthalpy, ITg, at the coil surface by
(h - h )
ai aa
al
where X = -S /w c R
o' pa
The surface temperature T corresponding to h" is readily found, and the leaving dry bulb tempera-
ture and sensible heat factor follow directly fran^the relations
_ -X
t = t +(t -t)e (15)
as s ai s '
SHF = c (t - t )/(h - h ^) (l6)
p ai a2 ' ai as' ^ '
Once the coil size has been determined, fin and tube costs can be calculated based on unit material
costs furnished as input. Labor costs may also be included provided information is available which re-
lates the time required for coil fabrication to the various gecsnetric parameters. Obviously, labor costs
will vary greatly depending upon manufacturing methods, plant layout, production volumes and other factors
and generalized relationships cannot be given.
h. Iterative Procedures
An important consideration in the development of computer programs for designing heat exchangers is
the selection of iterative procedures which converge quickly and consistently to a correct solution. In
the present program iterative procedures are involved in solving eq (5) for surface temperatures, and al-
so to find coil size or cfm to match the specified load. A discussion of these procedures is given below
^.1 Surface Temperatures
"When the derivative of f (x) is a simple expression and easily found, the real roots of f(x) = 0 can
be computed rapidly by a process called the Newton-Raphson Method" (l^) . According to this method,
successive approximations to the root can be formed by the following steps.
a, = a - f (a )/f' (a )
1 o ^ o" o'
a = a - f (a )/f' (a )
a^ = a - f (a ) /f' (a )
n n-i n-i'' n-i'
where a^ is the first approximation to the root. Applying this procedure to eq (5) we obtain
fCtg) = t3 - tr - C (h^ - hg) = 0
534
Therefore
f (t ) = 1 + C h.
-t - t - C(h ~h)
t (new) = - (-^ £ 5 '—\ (17)
s s
1 + C h '
s
Since f'(tg) is always greater than unity, a routine based on eq (l?) will always converge rapidly.
Following are a series of FORTMN statements based on eq (l7) which can be used to calculate sur-
face temperature to within E degrees of its correct value.
C = (RR + RM)/( .2^3*RA)
TS = TR
1 CALL HAIR (TS, P, HS, HSP)
DT = (TR-TS + C* (HA. - HS) j/(l. + C * HSP)
TS = TS + DT
IF(ABS (DT - E) ) 2, 2, 1
' 2 CCWTINUE
In the above routine HAIR is a subroutine which calculates air enthalpy at saturation (hs) and its
derivative (HSP) as a function of surface temperature (ts) and air pressure (p) .
h.2 Air Flow Rate
As previously described, the program may, in some cases, be called upon to match the load by varying
the coil length between tube sheets, with the air face velocity held constant. In other cases the air
flow rate is varied to match the load while holding the coil size constant.
Let us first consider the case where the coil size is fixed. Figure 6A is a graph showing for a
typical case how the coil capacity q as calculated by the program will vary with the assumed flow rate w.
Note that as flow rate increases the capacity asymptotically approaches a maximum value. This is the
value corresponding to negligible air-side thermal resistance; it must be greater than the given load if
a solution is to be found.
As the air quantity decreases, the capacity approaches zero at a finite value of air flow equal to
Wq. This is due to a decreasing enthalpy difference (approach) at the leaving air side of the coil.
This zero approach condition is possible because the leaving air enthalpy, hg^^, is calculated as a
function of the given load, q^, rather than as a function of the calculated capacity, q, since the latter
is not known at the beginning of the computation.
Figure 6b is a similar plot to figure 6a for the case where the length between tube sheets is varied
to match the load. In this case the calculated capacity can reach a maximum and th^ decrease with in-
creasing length and flow rate. The decrease occurs when the effect of refrigerant-side pressure drop be-
comes dominant. Obviously, the given load must be below this maximum value if a solution is to be found.
Depicted graphically on figure 6b is an iterative procedure which can be used in both of the above
cases to find the value of w for which q = q . The procedure calculates successive approximations to w
by interpolating along a straight line between the points (O, Wq) and (q^j, w^) . A general equation re-
lating the new value of flow rate, Wj-^+j^, to the previous value, Wjj, follows directly.
w = w + (w - w ) —
n+1 o ' n o q
n
Although convergence is not particularly rapid with this procedure, it offers the important advant-
age of insuring convergence for all values of w^ less than w^.
535
5. Sample Output
Figure 7 gives the output corresponding to the input provided in figure 1. In addition to the cal-
ciilated quantities for the dimensions and performance of the coll, most of 'the input data values are re-
corded also. This is to assist the user in identifying the coil design and in making comparisons and
selections. Comparisons are also .facilitated by the columnar format used for output.
In the example given the program was asked for solutions at only one air velocity, ^50 ft/min. Three
solutions were given. As a first choice the prograjn arrived at a design with 2h tubes in the face and 12
circuits. It then increased the tubes in the face to 26 and selected 15 circuits. Finally, the tubes in
the face were reduced to 22 and a solution given for 22 circuits. In this last case 11 circuits was re-
jected by the program as being beyond good design practice; the search for a solution at a greater number
of circuits resulted in 22 as the only number which would meet the requirements that N^/n^ be an integer.
The last case illustrates a situation where designer selection of the number of circuits may result
in an improved design. If, for example, space limitations dictate a maximum of 22 tubes in the face the
designer may wish to override the program by specifying the number of circuits at some value between 11
and 22. While this may present a more difficult circuit balancing problem, it could result in a more
economical design.
An important constraint which frequently is imposed is the cfm/ton. As presently written the pro-
gram starts with a value of cfm/ton dependent upon the refrigerant temperature and the entering air en-
thalpy. The final value will show variations from this initial selection, depending on the ratio of the
design load to the first trial value of the calculated load. To arrive at or near a specific cfm/ton,
therefore, some trial and error computations may be necessary involving face velocity, fins per inch,
number of tube rows or face area. Here again the designer's experience and judgment plays an important
role in arriving at a good final choice.
From the foregoing it is clear that the program described here is a powerful design tool. It has
made practical the application of improved fundamental relationships, and more accurate design procedures.
As our understanding of the fluid flow and heat transfer processes is increased through new research re-
sults, modifications can be made to reflect that improved knowledge. In this way the program plays an
important role in accelerating the process of bridging the gap between research results and engineering
application .
Acknowledgement
The authors express their gratitude to Mrs. Anna D. Mathill of the Mathematics Section, Research
Division, Carrier Corporation, for her major contributions to the development of this program.
6. References
(1) Anderson, S. W., Rich, D. G. , and Geary, D. F.:
Evaporation of Refrigerant 22 in a Horizontal
5/^ inch 0. D. Tube. (ASHRAE Transactions,
Volume 72, Part I, I966, p. 28).
(2) Standard for Forced Circulation Air-Cooling and
Air-Heating Coils, (Air Conditioning and Refrig-
eration Institute, Standard ^10-64).
(3) Methods of Testing for Rating Forced-Circulation
Air-Cooling and Air-Heating Coils (American
Society of Heating, Refrigerating and Air-
Condi tioning Engineers, Standard ^J>-6h) .
(h) Carrier, W. H. , and Anderson, S. W.: The Re-
sistance to Heat Flow Through Finned Tubing
(Heating, Piping and Air Conditioning, May
19^^, p. 504) .
(5) Rich, D. G. : The Efficiency and Thermal Resist-
ance of Annular and Rectangular Fins (Proceed-
ings of the Third International Heat Transfer
Conference, Vol. Ill, I966, p. 28l) .
(6) Handbook of Fundamentals, Chapter 3, Heat
Transfer (American Society of Heating, Refrig-
erating and Air Conditioning Engineers, ) .
(7) Pierre, Bo: (Kylteknisk Tidskrift, Volume 3,
May , p. 129).
(8) Altman, M. , Norris, R. H. , and Staub, F. ¥.:
Local and Average Heat Transfer and Pressure
Drop for Refrigerants (ASME Transactions,
August i960, p. 189) .
(9) Johnston, R. C, Jr., and Chaddock, J. B. :
Heat Transfer and Pressure Drop of Refrigerants
Evaporating in Horizontal Tubes (ASHRAE Trans-
actions, Vol. 70, 196k).
(10) McAdams, W. H. : Heat Transmission, McGraw-Hill
Book Co., New York, 195^, 3rd Ed.).
(11) Lockhart, R. W., and Martinelli, R. C: Pro-
posed Correlation of Data for Isothermal Two-
Phase Two-Component Flow in Pipes (Chem.ical
Engineering Progress, Vol. 19*^-9, P- 39)-
536
(12) Martinelli, R. C. and Nelson, D. B. : Prediction (l^) Scarborough, J. B. : Numerical Mathematical
of Pressure Drop During Forced Circulation Analysis (The Johns Hopkins Press, ,
Boiling of Water (ASME Transactions, Vol. 70, 2nd Ed.).
19^5, p. 695).
(15) Pierre, Bo: Flow Resistance with Boiling Re-
frigerants (ASHRAE Journal, September and
October, ).
537
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538
DESieN OF DIRECT EXPANSION EVAPORATOR COILS
PROSRAM 0X-I2/Z2
Figure 2 Main Program Flow Diagram
539
HIGH LOADING
LOW LOADING
CIRCUIT LENGTH
Figure 3 Heat Transfer Coefficient and Temperature Versus Circuit Length for an Evaporating
Refrigerant in a Tube
540
.REFRI6.
OUT
,REFRIQ.
OUT
REFRIG
IN
REFRIG.
IN
THERMAL PARALLEL FLOW
B
THERMAL COUNTERFLOW
(s « SUPERHEAT TUBe)
Figure h Two Evaporator Circuiting Arrangements
541
542
A FACE AREA CONSTANT
B FACE VELOCITY CONSTANT
Figure 6 Calculated Capacity Versus Assumed Air Flow Rate
543
COOLING MD DEHUMIDIPYING COIL DESIGN DX-12/22
DESCRIPTION'
SAMPLE
RAMPT.F
^ ur\ V J-j ui iDJ-jiv
J
TDTT -po T (^Tjyp A Torn
22
22
Cel.
FTWR P"R"R TNPH
X .l.AM 1—' J. 1 1 w J.i
1 ^ n
J.^ « u
"1 n
IMTTMRPP CW PnWC;
1*1 U r>~' r\ \Jr i\ UVv o
z
J
J
TT TP.'W TP A CV ^ PA r TWTi
1 PRn
X U
TUBE ROW SPACING
INCHES
1.083
1.083
1.083
TUBE O.D.
INCHES
.520
.520
.520
m 7
. Ul f
.
.
• i'?
•
ATR WT OPTTVC '^TTl'l
riXn V Hi XiVA-f XIX \>J XU J
PPM"
CVM( 9>TT))
CFM
7Q^P
A-TD PRRRRTTR'R
IN . HG
2Q Q?
PQ OP
PQ OP
TVrriMR'F'R (W TTTRTilf? TTJ "PAfP
vi Ui"lXXtjX\ \J1: ± UlJX-iQ X-LN Prl-'^ylj
2h
26
22
X3
00
NUMBER OF RETURN BENDS
24
26
22
COIL HEIGHT
INCHES
30.00
32.50
27-50
LENGTH BETWEEN TUBE SHEETS
INCHES
8i^.6l
77.61
95.84
SURFACE RATIO
20.3
20.3
20.3
RTTRTOPF /"PAPF /rDW
Pli 7
pit 7
JjUHU
I5XU / rlrv
p iinnnri
P iinnnn
SUCTION TEMPERATURE
DEGF
^2 . 0
^2 . 0
4-2 . 0
rOMD T.TQ TEMPRRATTTRF
DEGF
110. 0
110 . 0
Tin n
QTTpTTRHFAT
DEGF
12 . 00
12 . 00
12 . 00
VJiVX / J.\J-JX X\ • X'XX U \ V"i /
DEGF
10.23
10.81
1 56
QTIPP /pT?|TO MTTl f RTTPHTI
iJ UX^X^ / X\Xjr X\ • vi±U \ OU JTIIX y
DEGF
1 ^
J-^ .
13.68
it 65
ENT. DRY BULB TEMPERATURE
DEGF
80.00
80.00
80.00
ENT. WET BULB TEMPERATURE
DEGF
67.00
67.00
67.00
LVG. DRY BULB TEMPERATURE
DEGF
fin
LVG. WET BULB TEMPERATURE
DEGF
S7 4S
S7 8q
TADP
DEGF
7il
ss 66
sfi PO
AIR TH.RES.(STD) HR-SQFT-DEGF/ BTU
(
(
• '-'1(1
AIR PRESSURE DROP(ACT) IN. WATER
.268
.268
.268
METAL RESISTANCE HR-SQJT?-DEGF/BTU
.
.
.
REFR.COEFF (EVAP) BTU/HR-SQFT - DEGF
655
6i4
451
REFR.C0EFF(SUEHT)BTU/HR-SQFT - DEGF
82
77
sn
REFR. MASS VELOCITY LBS/HR/SQFT
REFR. TEMP. DROP
DEGF
6. 08
h 87
1. 08
FACE AREA
SOFT
17.63
17.52
18.30
SUPERHEAT LENGTH
FEET
h nn
SENSIBLE HEAT FACTOR
7SP
.766
CFM PER TON
597
412
FIN MATERIAL COST
DOLLARS
27.87
27.70
28.94
HAIRPIN TUBE COST
DOLLARS
55.62
55.38
57.61
TOTAL MATERIAL COST
DOLLARS
85.89
85.68
88.75
FIGURE 7 SAMPLE OUTPUT
544
Simulation of a Multicy linder
Reciprocating Refrigeration System
with Chilled Water Coil and
Evaporative Condenser
E. Stamper and M, Greenberger'''
Newark College of Engineering
Newark, New Jersey 0
A refrigeration system consisting of a packaged chiller, chilled water coil,
and evaporative condenser was simulated mathematically in an effort to determine
it's performance under varying load conditions. While the simulation was done for
the above system only, the method used is sufficiently general to be applied to re-
frigeration systems with other components. Components were selected from manu-
facturers catalogues to meet design load conditions for an assumed building whose
load is time dependent. The response of the refrigeration system to these changing
building loads is found by simulating the performance of each component by a
polynomial function of two independent variables and solving for the balance point
by matching the polynomials.
The water coil's performance is expressed by finding its effectiveness as
a function of air and mass flow rates. The chiller's performance is given in terms
of the leaving chilled water temperature and condensing temperature. The evapor-
ative condenser's performance is a function of the condensing temperature and out-
door wet bulb temperature.
Manufacturer's catalogue data were used with a computer program to deter-
mine the nine constants needed in the polynomial expressions for each system
component and the system balance was then established using a computer program
for each load on the system.
Key Words: Simulation, system simulation, refrigeration system simulation,
component simulation.
1. Introduction
The calculation of energy requirements of a building and the use of a computer to control the start-
ing and stopping of components of the building's air conditioning system require the simulation of the
performance of both the air distribution system and the refrigeration system. Methods for calculating
building cooling and heating loads via computer have been developed by the sub-committee on cooling and
heating loads of ASHRAE's Task Group on Energy Requirements for Heating and Cooling and presented in the
publication of this sub-committee [1]^. Suggested methods of component simulation and forms of the
equations to be used were presented in the publication of the Task Group's sub-committee on System Simu-
lation [2]. An example of the simulation of a dual duct system is also given in that publication.
This paper uses the methods suggested for component simulation to simulate the performance of a
multicylinder reciprocating compressor water chiller, evaporative condenser and chilled water coil. The
output of the calculations give air flow over the cooling coil, coll bypass factor, coil effectiveness
as well as power input to the compressor, total heat rejection, condensing temperature as well as per-
cent of the time that the compressor is running.
"Professor of Mechanical Engineering and Graduate student, currently Desalting Engineer, Mekorath
Water Co., Israel, respectively.
'Figures in brackets indicate the literature references at the end of this paper.
545
2. Cooling Load
2.1 Building
It is necessary to have cooling load data in order to select equipment to meet the design load as
well as to determine how the equipment will perform under part load conditions. The fictitious building
shown in figure 1 was used to calculate the cooling loads . The building was located in New York City
and is three stories high with wall, roof and glass areas and construction indicated in the figure.
2.2 Cooling Load Calculation
The cooling load was calculated by hand at two hour intervals from 7 A.M. to 7 P.M. for two typical
days, July 21 and August 21. The calculations were based upon recommended procedures in the ASHRAE
Handbook of Fundamentals [3]. A typical outdoor temperature variation was taken from figure 15.16 in
Threlkeld [4]. The number of people assumed to work in the building Is 375, starting between 7 and 9 A.M.
and leaving between 5 and 7 P.M. The lighting load was assumed constant at 4.75 watts ft."^. Outdoor
design conditions are 94F dry bulb and 77F wet bulb. To allow for vacations 80% occupancy was assumed
for the July 21 calculation. Outside air is introduced at the rate of 15 cfm per person and at the
outdoor weather conditions.
Results of the load calculations are in Tables 1 and 2. These results were used in selecting the
components and were used in determining the necessary operating conditions for each component under
part load.
Table 1
Sxjmmary of Cooling Load for August 21
Sensible Load 7 9 11 13 15 17 19
a. Transmission
Roof -18,202 -17,971 - 2,304 21,888 61,517 76,262 71,885
North Wall - 5,400 - 4,140 360 4,860 8,640 11,520 10,440
West Wall 840 2,040 4,200 6,360 8,280 9,720 11,760
East Wall - 9,083 ~ 6,896 841 8,746 14,968 17,491 15,809
South Wall -12,334 -10,765 - 9,157 2,018 10,316 17,268 19,062
b. Transmitted Solar Radi-
ation & Transmission
East Windows 28,200 62,150 59,506 40,727 47,025 70,548 56,272
South Windows 15,635 16,592 40,743 67,864 71,682 50,330 27,709
South Door 10,992 13,552 33,440 59,904 57,320 39,136 20,304
c. Internal Load
Infiltration 781 540 1,404 1,836 2,052 1,944 3,384
Lights 471,400 471,400 471,400 471,400 471,400 471,400 471,400
Fan Motor 30,528 30,528 30,528 30,528 30,528 30,528 30,528
People - 93,750 93,750 93,750 93,750 93,750
Total Sensible Load 513,357 650,834 724,711 809,881 877,478 889,897 738,553
2 . Latent Load
Infiltration 12,481 4,889 4,017 3,533 3,340 3,436 8,515
People - 75,000 75,000 75,000 75,000 75,000
Total Latent Load 12,481 79,889 79,017 78,533 78,340 78,436 8,515
3. Ventilation Load 316,406 315,141 313,875 312,609 311.344 311,344 313.875
4. Total Cooling Load 842,244 1,045,864 1,117,603 1,201,023 1,267,162 1,279,667 1,060,943
546
Table 2
Sunvmary of Cooling Load for July 21
1. Sensible Load
11
13
15
17
19
Transmission
Roof
North Wall
West Wall
East Wall
South Wall
-28,570
-13,500
- 4,560
-16,651
-22,426
-28,339
-11,700
- 3,720
-14,464
-20,855
-14,285
- 9,000
- 1,680
- 7,905
-16,819
8,295
- 5,760
-720
- 1,177
-11,213
46,541
- 2,500
480
4,542
- 3,589
61,287
-180
1,920
6,560
2,691
57,830
0
4,800
6,063
5,382
Solar Radiation
and Transmission
East Window
South Windows
South Door
26,341
- 2,074
-588
52,877
5,599
5,536
59,383
27,139
22,680
35,821
43,359
36,752
61,482
29,939
24,376
57,601
11,897
9,352
30,540
3,525
2,804
Internal Load
Infiltration
Lights
Fan Motor
People
- 1,458
471,400
30,528
-540
471,400
30,528
75,000
108
471,400
30,528
75,000
324
471,400
30,528
75,000
540
471,400
30,528
75,000
432
471,400
30,528
75,000
208
471,400
30,528
Total Sensible Load
438,442
561,322
636,489 682,609 738,719 728,488 613,080
2. Latent Load
Infiltration
People
4,386
2,081
60,000
1,307
60,000
920
60,000
726
60,000
823
60,000
2,606
Total Latent Load
3. Ventilation Load
4,386
62,081
61,307
60,920
60,726
60,828
2,606
91,125
91,125
89,962
i,596
88,596
i,596
89,962
4. Total Cooling Load
533,953
714,528
787,758 832,125
884,041
877,912
705,648
3. Component Selection
3.1 Cooling Coil
The peak load occurs at hours (5 P.M. EDST) on August 21. The load is 1,279,667 BTU-hr""'' or
106.64 tons of refrigeration. Of this total the space sensible load is 889,367 BTU-hr"-'- and the space
latent load is 78,436 BTU-hr"-'-. To meet this load the water flow through the coil is given by eq (1)
Q = WC AT
P
(1)
where Q = total load (BTU-hr ""■) , C = 1.0 BTU-lb °F "''
p ^
AT = water temperature rise through the coil, F, taken as 10 for the selection made
W = water flow rate (Ib-hr . From eq (1)
W = J-'279^667 ^ 127,967 Ib-hr = 255.9 gal-min
The air flow across the coil (cfm) is given by eq (2)
1.08(T
T, )
Ivg.
(2)
547
. and T are the dry bulb temperatures before and after the coll
ent . ivg .
1 1.08(75-56)
A cfm
432 70
500
ft^ where a face velocity of 500 ft-min
Is used.
The coil face area required is FA =
12 coils with a length of 36" and height of 30" and a total face area of 90 ft^ and face velocity of
480 ft-min ^ were selected. From a manufacturer's catalogue to meet the required '^'g^
a set of 12, 6 row, 80 fins per inch coils 36" x 30" were selected.
1.18 tons-ft
3.2 Chiller
With the required tonnage of 106.64, leaving water temperature 45°F, entering water temperature of
55°F, two chillers were selected as possible alternatives. The simulation was run with both possibilities
to show how the simulation is helpful in selecting the optimum chiller to meet the building load char-
acteristics. The final selection is discussed under results. The two chillers selected had as full load
characteristics , for chiller A; saturated discharge temperature 103. 7°F, compressor power input 93.4 KW,
total heat rejection 133.4 tons; while for chiller B the corresponding values are 114. 3°F, 110.2 KW and
138 tons.
Each compressor is equipped with cylinder unloaders to operate at 100%, 75%, 50% and 25% of full load
capacity.
3.3 Evaporative Condenser
The evaporative condenser chosen with a saturation temperature of 103. 7°F, outdoor wet bulb of 77°F
would have a capacity of 133.2 tons with 20 sub-cooling. This was chosen to meet the conditions of
chiller A. This condenser has a capacity greater than the required 138 ton heat rejection needed for
chiller B at it's higher condensing temperature of 114. 3°F.
4. Component Simulation
Each component's performance is to be expressed as a function of two independent variables [2] in
the form:
Z = a^ + a2X + a^x + a^y + a^y
J. 2, 2_^22
+ a^xy + a^x y + agXy + a^x y
(3)
The coefficients a-^ through ag should be chosen so as to predict the performance of the individual
component over a wide range of load conditions. It is hoped that the manufacturers will present the per-
formance of their equipment in the form of eq (3). Currently this data is not generally available and
the coefficients used in simulating each component in this paper were computed from tabulated manufac-
turer's values (which are generally at or near full load). The equations so derived were used to predict
the part load performance. Clearly the results will be more reliable when more reliable part load data
becomes available.
4.1 Simulation of Chilled Water Coil
In accordance with the suggestions of Stoecker [2], the coil's performance should be given by the
effectiveness expressed as a function of the air flow (G) and water flow (W) rates.
The effectiveness is defined as
h. h
in
out Ah
h. - h Ah
in w w
548
where hj_^ and h^y^ are the enthalpies of the air before and after the coil and h^ is the enthalpy of
saturated air at the entering water temperature, so that Ah^ is an enthalpy potential.
The maximum possible effectiveness E =h. -h/h, -h where h = enthalpy of saturated air at
^ max m w In w w
the average water temperature.
The effectiveness can be expressed in terms of G and W because
Q = GAh = GEAh (5)
w
and q = W (T, - T ) = WAT (6)
in out
where AT, the cooling range is the water temperature difference across the coil.
In terms of the coil face velocity and face area
G = pVA (7)
For this example the coil was used as a "wild" coil, i.e. the temperature of the water entering the
coil and the mass flow of water across the coil is constant. Since the load on the coil is the building
load, and the outdoor conditions are known, and the water inlet temperature is constant, h^j^ is known and
h,^ is constant; the coil effectiveness can be computed from manufacturer's catalogue data. Therefore,
for a given coil with part load data given, the constants in:
2 2
E = a, + a„G + a-G + a.W + a^W
1 2 3 4 5
+ a^GW + a^G^ + a„GW^ + a.G^^ (8)
D / by
can be evaluated by solving nine simultaneous equations using manufacturer's data for G, W and computed
values of effectiveness based upon manufacturer's data.
4.2 Simulation of the Chiller
From manufacturer's data at full and part loads the chiller capacity, Q^-^ and power input, may
be expressed in terms of T^-^ and T^^^j, the temperature of water leaving the chiller, and the condensing
temperature of the refrigerant.
Q , = b, + b„ T , + b, T . ^ + b, T , + b, T ,^
ch 1 2 ch 3 ch 4 cd 5 cd
+ b, T , T + b_ T , ^ T , + b. T , T ,^ + b- T , ^ T ,^ (9)
6 ch cd 7 ch cd 8 ch cd 9 ch cd
2 2
P,=Ct+c„T+c„T, +c, T+c, T, +c, T,T,
ch 1 2 ch 3 ch 4 cd 5 cd 6 ch cd
+ c, T . ^ T , + c„ T , T ,^ + c- T , ^ T ,^ (10)
7 ch cd 8 ch cd 9 ch - cd
Again, standard programs for solution of simultaneous equations evaluate the constants if nine data
points are given.
The performance of the chiller is complicated by the fact that the compressor is equipped with un-
loaders to lower the power requirements in steps to 75%, 50% and 25% of full load requirements. However,
to deliver the exact cooling load the compressor must cycle and operate only part of the time.
549
The starting current is higher than normal running current so that the effect of cycling is to in-
crease equivalent power consumption; e.g. when the compressor operates say 80% of the time, the power
requirement is greater than 80% of the full time operating power. Manufacturers suggest that the ratio
of part time power required to full time power (RP) is expressible in terms of the percent time operat-
ing (RL) by
RP = R + .8 RL (11)
so that the heat rejected in the evaporative condenser is given by
Qrej = ^ + ^ (^ch^
4 . 3 Simulation of the Evaporative Condenser
The evaporative condenser heat rejection is given by:
QrEJ = '^l <^2("^^) + + '^4(V
2 2
+ d^ T J + d, (WBT) T „ + d^ (WBT) T
5 cd 6 cD 7 cD
+ dg (WBT) T^^^ + dg (WBT)^ (^cd^^ ^■'■^^
It is seen from eq.'s 10 through 13 that the power requirement of the chiller and heat rejected by
the condenser are functions of the condensing temperature, so that T^ will be determined by the relative
capacity of both components.
5. System Simulation
5.1 Control System
The coll was selected to operate without a control valve so that the water flow rate and entering
water temperature are constant. To control the output some of the air is bypassed around the coil and
then at low loads the amount of coll surface exposed to the air is decreased.
The blocking of part of the coll surface is necessary because at low air flow rates the leaving air
temperature becomes uncomfortably low.
In the mathematical model the requirement of blocking part of the coll may be sensed by values of E
that are too high, approaching E^^^ (the DBT of the leaving air approaches the average water temperature).
5.2 Mathematical Model
At a given load eq.'s (8) and (5) must be satisfied simultaneously. Since W is constant, eq . (8) may
be rewritten as:
E = B' + F'G + D' G
where B ' = a. + a.W + a^W
14 5
(14)
F' - a^ + a,W + a^W
ZD o
D' = a^ + a^W + agW
550
GE
Using the identity G = ^ in eq (14) we get:
E"' - B'E^ - (GE)F'E - (GE^)D' = 0
This equation is solved for E with constant G such that
0 < E < E
max
If no such root exists, G is reduced (part of the coil is blocked) until such a root is found.
The operation of the packaged chiller and evaporative condenser is dependent upon the cooling load
and the outdoor wet bulb temperature only. If the chiller leaving water temperature is fixed, the con-
densing temperature T^^^ is the only variable.
The capacity of the chiller is: Q , = f(T , , T ,) , if T , is fixed at 45°. Based on the actual
^ chil ch cd ch
load Q the number of cylinders required is found.
For example if :
RL = Q/Q , = 0.6
chill
so .50 < RL < .75, 75% of the cylinders are required and the percent operating time is:
RLI = (100) = 80%
The power ratio is then RP = .2 + .8RLI = .84 and the actual power required
PWI = P , X .75 X .84 = .63 P ,
ch ch
P , = f (T , T ^) and Q„^^ = Q + PWI
ch cw cD REJ
The capacity of the evaporative condenser is evaluated at T^^
Q = f(WBT, T „) and the two values are compared,
evcon cD
If Q > Q . then T „ is decreased and if Q < Q . , T „ is increased,
^evcon rej cD evcon rej cD
A flow chart of the computer program is shown in figure 3.
6. Results
Typical results are shown in Tables 3 and 4 for the full load case on August 21 and 5 P.M. The
two alternate chillers chosen result in an input of 94.3KW with all cylinders in operation 100% of the
time, and 96.4KW with all the cylinders in operation 91.9% of the time. The result for the full load
period are typical throughout. One chiller chosen generally has a smaller power input and cycles less
often. Thus, the simulation is helpful in equipment selection as well as in energy computation.
An exception to the first alternate giving better results is shown in Tables 5 and 6 where the out-
puts at 9 A.M. July 21 are presented. Here alternate 2 has a lower power input and will cycle less.
The importance of examining the entire range of outputs is evident.
551
Table 3
Date - August 21
Time - 17.00
Cooling Load, BTU/HR .
Outdoor Dry Bulb Teinp.,F 93.0
Outdoor Wet Bulb Temp.,F 77.0
Water Coil Data
Percent of Face Area Used 100.0
Water Temperature (Entering Cooling Coil) ,F 45.0
Water Flow In Cooling Coil,GPM 255.9
Air Temp. (Entering Cooling Coil) ,F 77.0
Air Flow Over Cooling Coil,CFM A.
Coil Effectiveness Is 0.571
Bypass Factor Is, Percent 15.8
Water Chiller Data
Water Temp. Living Chiller, F A5.0
Condensing Temp, of Chiller, F 103.7
100 Percent of Cylinders are in Operation
Operating 100.0 Percent of the Time
Actual Power Requirements ,KW 94.3
Total Heat Rejection, Tons 133.4
Table 4
Date - August 21
Time - 17.00
Cooling Load, BTU/Hr .
Outdoor Dry Bulb Temp.,F 93.0
Outdoor Wet Bulb Temp.,F 77.0
Water Coil Data
Percent of Face Area Used ■ 100.0
Water Temperature (Entering Cooling Coil) ,F 45.0
Water Flow in Cooling Coil,GPM 255.9
Air Temp. (Entering Cooling Coil) ,F 77.0
Air Flow Over Cooling Coil,CFM , 420 76.
Coil Effectiveness Is 0.571
Bypass Factor Is, Percent 15.8
Water Chiller Data
Water Temp. Living Chiller, F 45.0
Condensing Temp, of Chiller, F 103.7
100 Percent of Cylinders are in Operation
Operating 91.9 Percent of the Time
Actual Power Requirements ,KW 96.4
Total Heat Rejection, Tons 133.4
552
Table 5
Date - Ju;Ly 21
Time - 9.00
Cooling Load, BTU/HR .
Outdoor Dry Bulb Temp.,F 70.0
Outdoor Wet Bulb Temp.,F 67.0
Water Coil Data
Percent of Face Area Used 75.0
Water Temperature (Entering Cooling Coil),F 45.0
Water Flow in Cooling Coil.GPM 255.9
Air Temp. (Entering Cooling Coil),F 74.4
Air Flow Over Cooling Coil.CFM .
Coil Effectiveness Is 0.724
Bypass Factor Is, Percent 59.6
Water Chiller Data
Water Temp. Living Chiller, F 45.0
Condensing Temp, of Chiller, F 91.9
75 Percent of Cylinders are in Operation
Operating 68.1 Percent of the Time
Actual Power Requirements ,KW 48.9
Total Heat Rejection, Tons 73.4
Table 6
Date - July 21
Time - 9.00
Cooling Load, BTU/HR .
Outdoor Dry Bulb Temp.,F 70.0
Outdoor Wet Bulb Temp.,F 67.0
Water Coil Data
Percent of Face Area Used 75.0
Water Temperature (Entering Cooling Coil) ,F 45.0
Water Flow in Cooling Coil.GPM 255.9
Air Temp. (Entering Cooling Coil) ,F 74.4
Air Flow Over Cooling Coil.CFM .
Coil Effectiveness Is 0.724
Bypass Factor Is, Percent 59.6
Water Chiller Data
Water Temp. Living Chiller, F 45.0
Condensing Temp, of Chiller, F 91.7
50 Percent of Cylinders are in Operation
Operating 94.1 Percent of the Time
Actual Power Requirements ,KW 45.4
Total Heat Rejection, Tons 71.9
553
7. References
Proposed Procedure for Determining Heating and Cooling Loads for Energy Calculations. Task Group
on Energy Requirements for Heating and Cooling - ASHRAE , edited by M. Lokmanhekim .
Proposed Procedures for Simulating the Performance of Components and Systems for Energy Calculations.
Task Group on Energy Requirements for Heating and Cooling - ASHRAE, edited by W. Stoecker.
Handbook of Fundamentals, , ASHRAE.
Threlkeld, L. James, Thermal Environmental Engineering, Prentice Hall, .
Naylor, T. H., Computer Simulation Techniques, W. Ley, .
554
ROOF - MEDIUM CONSTRUCTION, 2" INSULATION
2" GYPSUM PLANK.
10* CEILING
1st FLOOR
13 BRICK
PARTY WALL
X
80'
120'
WINDOWS
27 % GLASS
ENTRANCE DOOR
100% GLASS
EAST
8 CONCRETE
^ITH 5/8" PLASTER
2nd a 3rd FLOORS
WINDOWS
27% GLASS
Figure 1. Building Orientation and Structure
555
556
Use of Digital Computers
For the Heat and Mass Transfer
Analyses of Controlled
Environment Greenhouses
M. Kudret Sel^uk, Ph.D.
Environmental Research Laboratory
University of Arizona
Tucson, Arizona
Heat and mass balance equations for the controlled-environment
Greenhouses yielded simultaneous non-linear differential equations
that were modified to finite difference equations for computer
solution. These equations were linearized before attempts were
made to solve them, using a CDC Computer. The unsteady state
analysis was carried out to determine the variation of temperatures
due to storage effects, especially that of soil. The plastic cover,
plant and air temperatures responded to any change of radiation or
external disturbance fast enough to justify a quasi-steady state
analysis in which the radiation level was modified step-by-step in
hourly intervals . Various programs were written to solve the problem
at different phases; namely, the analysis without any moisture effects,
studies with transpiration taken into consideration and, ultimately,
the model with evaporation from the soil, transpiration from the
plants and condensation over the plastic cover whenever its tempera-
ture drops below dew point of the air stream. Since the final phase
covers all phenomena involved, only its formulation and computer
programming are emphasized. The computer programs developed may
be used in predicting the controlled-environment greenhouse perfor-
mance under continuous operation conditions for any locality, if
weather data are supplied. This information also will enable the
designer to determine the capacity of the packed bed humidifiers,
circulation fans and water requirements of humidifiers and irriga-
tion purposes.
Key Words: Controlled environments, greenhouse energy
budget program, greenhouse heat and mass balances.
1. Introduction
The controlled-environment greenhouse is the vital component of the POWER-WATER-
FOOD complex developed by the University of Arizona. The principle of operation and
features of a large-scale scheme which is being applied in Abu Dhabi on the Arabian
Gulf already has been reported. [1], [2], [3]^
The present paper outlines the computation methods and details of the computer
programming of an extensive study of the heat and mass balances of the controlled
environment greenhouses [4].
■'"Author is an Assistant Professor at the Mechanical Engineering Department
Middle East Technical University of Ankara, Turkey. This paper is based upon
a research carried out while he was on leave at the Environmental Research
Laboratory of the University of Arizona.
2
Numerals in brackets refer to references at the end of this paper.
557
2. Mathematical Models
The formulation of the heat and mass transfer in the inflated plastic controlled-
environment greenhouse was carried out at a number of stages, from simple to elabo-
rate. The purpose has been to obtain approximate values of unknowns for use in the
iterative process to compute temperatures and moistures accurately.
Fig. 1) is a sketch of the greenhouse, its dimensions and definition of unknowns
investigated as well as initial and boundary conditions .
The ambient db and wb air temperatures, outside wind velocity, inside air
velocity, solar radiation intensity and initial db and wb air temperatures are
specified as input data for the computer program. The present analyses enable one to
compute temperatures of the plastic cover, air stream plant leaf surface temperatures,
soil temperature at the surface and various levels below the surface, at selected
space intervals for a 24-hour operation period.
The following steps were taken in formulating the problem:
(a) The analysis of the system neglecting the moisture effects, steady state,
(b) The analysis of the system with plant transpiration only, steady state,
(c) The analysis of the system neglecting the moisture effects, unsteady state,
(d) The analysis of the system with plant transpiration only unsteady state,
(e) The analysis of the system with the effects of soil moisture evaporation,
plant transpiration and condensation on the cover, unsteady state,
(f) An analysis to predict the greenhouse performance for year-round operation
based upon the formulation (e) .
Since the detailed description of these formulations would be too lengthy, only
the study which is covered in formulation (e) will be outlined.
It should be noted that formulations (a) through (d) are special cases of formu-
lation (e) in which some of the parameters have been neglected and analysis is applied
to the steady state operation.
2.1 The Analysis of the System with Soil Water Evaporation,
Plant Transpiration and Condensation on the Cover
The model employed in this analysis is outlined in Fig. 2) . The computer program
is labeled KUD 81.
2.1.1 Heat Balance on the Cover
Neglecting the heat capacity of plastic cover and employing quasi-state analysis:
hc.PAx(T, - e ) + K PAxh^ (a)-aj)+hr E^e^A{e- e^)F ^
1 1 c c fg a c p,c p,Lw c,Lw pr p c p,c
+ la PAx + hr e ^ e ^ F PAx{e - 0 ) = he PAxO - T )
c,sw s,cs,Lwc,Lws,c s c w c a
+ hr , PAx (9 - T , ) e ^ , -, .
c,sk c sky c,Lw (i)
-1 -2
where K is the condensation rate in (lb hr ft )
c
Taking F , F =1, and from F • e =p*.
^ p,c' s,c
Rearranging for the unknowns of 6 T, 6 and G and dividing by Ax:
c , 1 , p s
[-hc.P - hr Fa /Ax - hr F P - he P - hr , pe , ]e
1 p,c p,c pr s,c s,c w csk'^ CLw* c
+ [hc.P]T, + [hr F A /Ax]6 + [hr F P]e = - k Ph^ (o) - (o )
1 1 P,c p,c pr' -' p '- s,c s,c s c f g ^ a c'
- la P - he PT - hr , Pe ^ T ,
c,sw w a c,sk c,Lw sky (2)
558
Mass Balance of Airstream, enables one to obtain w in terms of w , o) , u and
the initial humidity ratio of the airstream (o) . ) . P
a / 1 n
2.1.2 Mass Balance on Airstream
Change of water vapor content of the airstream is :
m(a) - oj .)=K(a)-a))A + KA(w -a))-K(u -w )PAx (3)
a a a,in ssagpppa cac
The transpiration rate is proportional to:
K = — i
P
1 + R ^
-T-r 77; StOm
(he /C
P Pm
o -1
and R ^ is stomatal resistance in (hr ft lb )
stom
Rearranging (3) and solving for (o) ) ;
a
0) =(mio . +Ka)A tKAw + Ka) PAx)/{ra + KA + KA + K PAx) (5)
a a a,in ssg PPP cc a sg pp c
from the Psychrometric Relations, assuming saturation conditions at the cover, leaf
and soil surfaces :
0)
[0.622 P ,„ , ]/[P - P ,Q , ] (6)
V (9c) ' '- m V (6c)
[0-622 P„,«^J/[P^ - P,w«^J (7)
p ■ V ( Op) '- m V ( 6p)
0) = [0.622 P ,9 ,]/[P - P ,Q x] (8)
s"- v(s) '-m vOs)-"
Equations (5), (6), (7) and (8), together with 4 heat balance equations correspon
ding to cover, airstream, plant and soil are 8 non-linear simultaneous equations
which should allow one to solve the unknowns a),a),a),w,6,T,,6 and 6 .
p c s a' c l p s
To ease the solution, u^, and to^ will be expressed as linear functions of temper-
ature in the form of co = X9 + Y. Rather than using relations (6) , (7) and (8) , the
constants X and Y are to be individually determined within the temperature region of
interest.
For the cover at saturation conditions: u = X 6 + Y
c c c c (9 )
For the plant at saturation conditions: w = X 6 + Y (10)
P P P P
For the soil at saturation conditions: w = X 9 + Y (11)
s s s s
9 , 9 and 9 were approximately determined employing the analysis with plant transpi
ratioR only.^ Details of this analysis are described in another publication by the
author [5]. The coefficients X , X , X , Y , Y , and Y can be closely estimated
■' c p s c p s ^
from the saturation curve for air-water vapor mixture once 9 , 9 and 9 are known.
c p s
Since the mass flow rate is:
m = p vA : Ib/hr
a '^m s '
The mass balance equation (5) for the airstream then could be written in terms
of temperatures alone:
'^a=[^(Pm^\/A^)'^a,in + (KsV^^^^ ^""s^s + ^s^ + ^Vp^^''^ ^""p^P ^P^
+ K P(X 9 + Y )]/[p VA /Ax + KA/hx + K A /Ax + K P] (12)
559
separating 9^, 9^ and 9^,
w = -, ^ — 77 , ^ — y,-*- ^ ^ — 77 ^ ^, [X K P9 + (X K A /Ax) 9 + (X K A /Ax)
a (p vA /Ax + K A /Ax + K A /Ax + KP)'-cc c PPP P sxg'
ms Sg PP C r r r- c
+ (p vA /Ax) 0) . +YKP + YKA /Ax + Y K A /Ax] (13)
m s a,in c c PPP s s g' ■'
Substituting u from equation (13) and w from equation (9) , into equation (2) :
[ - hc.P - hr F A /Ax - hr 7^ P - ho P - hr^ „vPe^ n„]e + [hc.P]T.
1 p,c p,c pr' s,cs,c w CjSKclwc i i
+ [hr F A /Ax]9 + [hr F P]9 = -K Ph, [d{X K P 9 + (X K A /Ax) 9
'- p,c p,c pr p ^ s,c s,c s c fg'- c c c P P P P
+ (X K A /Ax) e + ( p vA /Ax)a) . +YKP + YKA /Ax + Y K A /Ax} - X 9 - Y
ssg' s '^ms a, in cc PPP sag' cc
- la P - he PT - hr , Pe ^ T ,
c,sw w a c,sk c,Lw sky (14)
Where _ 1
p vA /Ax + K A /Ax + K A /Ax + K P
^m s' s g' p p' c
2.1.3 Heat Balance on Airstream
For a system of Ax length:
m C (T, - T, . ) = he A (9 - T,) + he A (9 - T, ) - he.PAx(T, -9 )
apm l l,in sg s 1 pp p 1 i 1 c
For unit length:
(p v/Ax)A C (T, - T, . ) = he A /Ax(9 - T, ) + he (A /Ax) (9 - T, )
m s pm 1 l,in s g s 1 P P P 1
- he^P(T^ - 9^) (15)
(A /Ax) : The effective plant surface per unit length of the greenhouse has to
be worRed out separately for the plant under study and at various stages of growth.
2.1.4 Heat Balance Over the Plant Canopy
The plant canopy does not have a definite geometrical shape, nor uniform heat
and mass transfer coefficients. The velocity field around and across the canopy is
not uniform. Therefore, those coefficients, areas, temperatures and velocities
have been bulked in this analysis. For the unit length of greenhouse, Ax = 1.
1^1 „a ^A^ + I ,T ,a ,A, = he A (9 - T, ) + h- K A (w - co )
D c,sw,D p,sw,D D,p d e,sw,d p,sw,d d,p PPP 1 P P P a
+ hr F A (9 - 9 ) + hr F A (9 - 9 )
s,p s,p p s p p,e p,c pr p c
+ hr,T^e^A(9-T,, ,,,,
p,sk e,Lw p,Lw pr p sky) (16)
where the subscript D refers to Direct, and d refers to diffuse.
(he A ) , (K A ) , (F A ) and (F A ) are bulked as indicated above.
P P P P s,p p ' p,c pr'
560
Substituting from equation (10) and co^ from equation (13):
n + I t a ,A, = he A (9 - T, )
Dc,sw,Dp,sw,DT),p ac,sw,ap,sw,da,p PP P 1
+ h _ K A [X e + y - D{ (X K P) 6 + (X K A /Ax) 6 + (X. K A /Ax) 6
fgpp'-pp p cc c PPP P ssg' s
+ (p vA /Ax)a) . + YKP + YKA /Ax + Y K A /Ax)]
^m s a,in c c PPP ssg-"
+ hr F A (9 - e ) + hr 'F A (9 - 6 )
s,p s,p p s p p,c p,c pr p c
+ hr ,T^e^A(9-T,,
p,sk c,Lw p,Lw pr p sky) (17)
2.1.5 Heat Balance on Moist Soil
The soil is assumed to be saturated to moisture. Evaporation from the soil surface
results in reduction of the soil surface temperature and affects the humidity ratio of
the airstream. The area of the exposed soil surface is the same for conduction con-
vection, radiation H.T. and evaporation.
In case of one-dimensional heat flow into soil, for unit soil surface dividing
by A
g
It a = h^ K (w - 0) ) + he (9 - T, ) + hr , e ^ t ^ (8 - T , ,
c,sw s,sw fg s s a s s 1 s,sk s,Lw c,Lw s sky)
+hr e.e^F (9-9)+ (hr A /A ) (9 - 9 )
s,cc,Lws,Lws,c s c s,p s,ppgs p
+ (V63)(e3 - 9^1) + P^^^c^o^ - e3,i^)/At (18)
Substituting w from equation (8) and w from equation (13):
S 3.
-h, K {X 9 + Y - D[X K P9 + (X K A /Ax) 9 + (X K A /Ax) 9
fgsss s '■ccc PPP P ssg s
+ (p vA /Ax)aj . +YKP + YKA /Ax + Y K A /Ax]} - he (9 - T, )
■^m s a,in c c PPP ssg' s s 1
- hr , e ^ T ^ (9 - T , ) - hr (9 - 6 )
s,sk s,Lw e,Lw s sky s,c s,c s c
- hr F A /A (9 - 9 ) - K (9 - 8 , ) /6 - p 6 C (8 - 8 . )/At
s,p s,pp g s p s s si s sss s s,in
= - It a (19)
c,sw s,sw
2.1.6 Heat Balance on the First Soil Slab
The first soil slab temperature after the time interval of (At) (^gj^)' c^^i be
obtained from:
(9 . , 9 ^ . - 29 , . ) = -|r(e 1 - 6 1 • ) (20)
s,in + s2,in sl,in aAt si si, in
or
o 2aAt[(9 . + 9 „ . )/2 - 9^, . ] + 8^, . -. .
8 , = —r-z— s , m s2,in sl,in-' sl,in (^0-1;
si 0
s
Similarly for the second soil slab:
®s2 = ^fp'^'^sl,in + ^s3,in^/2 - 632,11,^ + ^s2,in (20-2)
For the kth soil slab:
= ^[(e.,,_,, + 9^,,^,, ,J/2 - 8^^ ,J + 8^^ (20-k)
561
where (k;=m-4), and m is the number of unknowns. 4 equations refer to the cover,
stream of air, plant and the soil slab at the surface.
Those equations could be further simplified taking
(5 = /2aAt.
s
For 20 slabs below soil surface:
si
((
(6 . + e . . )/2
s , m s2 , in
s2
^sk =
^s20
si, in s3,in)/2
^^s,k-l,in + ^s,k+l,in'/2
3 -,„ . + 6 . )/2
sl9,in s21,in^
The initial and boundary conditions are;
"sky
1 , m
3 . e , . e „ e .
s , in , si, in, s2,in s21,in
li
a, m
(21)
(22-1)
(22-2)
(22-k)
(22-20)
The ambient air temperature
Effective sky temperature
Initial air temperature
Initial soil temperature profile
Initial humidity ratio of the airstream
Equation (14), (15), (17), (19) and (22-1) to (22-20) are 24 simultaneous equations
in which G , T, ,
are 24 unknowns to be solved.
C "1' p' s' si' s2' s20
The solution techniques and features of various programs follow.
Since the
tion also was
00 Series
KUD 0 3
10 Series
KUD 12
KUD 15
20 Series
KUD 21
50 Series
KUD 5 3
KUD 55
KUD 5 7
60 Series
KUD 61
3. Computer Programming
formulation of the problem was carried out at various stages, the solu-
obtained for the corresponding steps as listed in Table I.
Table I - List of Computer Programs
No-moisture Analysis, Steady State Printout + Variation of
(9^, T-^, 6^, 9^) along the Greenhouse, Computer Plotted
Analysis with Transpiration Only, Steady State Linear Interpolation for
the Plant Temperature Correction
Same as Above - Newton-Rhapson Method Used in Approximation
Same as KUD 15, Greenhouse End Effects Included
Unsteady State Analysis, No Moisture Effects 4 Equations + Schmidt-
Binder Technique
Same as KUD 53, but 4 Original Unknowns + 20 Soil Temperatures Solved
by 24 Equations
Same as KUD 53, but Design Modified for E.R.L. Tucson Greenhouses
Unsteady State with Transpiration only 4 Equations + Schmidt-Binder
Technique
562
Table I .- List of Computer Programs (Continued)
80 Series
KUD 81 Unsteady State, with Soil Moisture Evaporation, Plant Transpiration
and Condensation on the Cover 4 Equations + Schmidt-Binder Technique
KUD 82 Same as Above, Effect of Time Interval
KUD 84 Same as KUD 81, Effect of Stomatal Resistance
90 Series
KUD 91 12 Month Performance Prediction from KUD 81 Printout
KUD 92 Same as KUD 91, Result Computer Plotted
KUD 93 Same as KUD 92, Effect of Shading
3.1 The Analysis with no Moisture Effects
The formulation of the problem which is described elsewhere [4] yielded four
non-linear, simultaneous equations, due to the radiation terms of (9^ + 460)'' etc.
These were linearized using the equivalent radiation heat transfer coefficients,
hr , ....etc. The program is labeled KUD 03. The solution of this and other models
C , SK
was obtained using CDC Model computer, of the University of Arizona's Computer
Center.
(4x4) matrix A and 4 element column vector C were generated and the solution
of linear simultaneous equations was obtained using the Gauss-Jordan elimination
technique.
The computer program of the final model, however, includes the same matrix A
and vector C which is used to predict the temperatures of 6 , 6 and 9 .
c p s
3.2 Solution of the Model with Transpiration Effects Only
The formulation with transpiration effects which allows prediction of plant
temperatures more accurately has been described in Reference [5].
Starting with an estimated transpiration rate based upon the enthalpy potential
between the plant interface at approximate temperature and the airstream, both
transpiration rate and the final leaf temperature were iterated until the assumed
and calculated leaf temperature agreed with one another. The convergence of the
iteration was accelerated utilizing the Newton-Rhapson method as shown in Fig. 3) .
This process which utilizes the matrix E (4,4) and vector G(4) is included in the
second part of the computer program KUD 81.
3.3 Solution of the Model with Condensation on the Cover,
Transpiration from the Plant and Evaporation from the Soil
24 simultaneous equations previously derived were utilized. Those equations were
arranged for the 24 unknowns mentioned, and the coefficient matrix Q(24,24) and vector
Z (24) which are presented in Table II, were obtained. q corresponds to the matrix
element of Q(M,N) and z to z (M) .
563
Table II - Coefficient Matrix Q (24,24) and Vector Z(24)
for the Simultaneous Equations, Program KUD 81
Q{24,24) Z(24)
^11
^12
^313
^14
0
0
0
0
0
0 . .
^1
^21
"323
^324
0
0
Q
A
u
u
^2
^31
cr
^32
^33
^34
0
0
0
0
0
0
7
^3
^41
^42
q43
^44
0
0
0
0
0
0 . .
^4
0
0
0
0
1
0
0
0
0
0 . .
(6 . + e _ . )/2
0
1
0
1
1
0
\
1
0
0
1
1
1
I
1
0
1
1
0
1
1
0
1
1
0 . .
1
1
(e -, . +6 , . )/2
si , m s3 , m
1
0
1
1
I
1
0
1
1
1
1
0
I
1
1
1
0
1
1
1
1
0
1
!
!
1
0
1
1
1
0
f
1
1
1
0
1
1
1
0
t
f
1
f
1 . . .
1
1
1
1
1
1
(6 +6 ,,,.)
0 0 0 0 =(e,„.+e^, .)/2
sl9,in s21,in
The coefficient matrix Q and vector Z yield the final solution by means of
Gauss- Jordan elimination technique.
The other alternative is to solve the original 4 equations written for the cover,
airstream, plant and the soil surface slab, then apply the Schmidt-Binder method for
an hour's interval. The solar radiation intensity during an hour's period is assumed
to be constant. The soil surface temperature is determined starting with an initial
temperature profile following the method outlined in Reference [6].
Then, temperature profiles, at succeeding hours, within the soil are obtained at
intervals defined by At = 6|/2a.
The logic diagram of the computer solution is presented in Fig. 4) .
The ambient air temperature, solar radiation intensity, and the sky temperature
were supplied as boundary conditions.
The air outlet temperature from the control volume T, , was set equal to the
initial air temperature of the following control volume TT^^ in^ ' Similarly, the
solution of the present analysis w was introduced as the initial humidity ratio for
3.
the adjacent control volume. This process was repeated until the length of the
greenhouse was traversed.
Comparing the results obtained using these two approaches suggested for the soil
temperature profiles, it can be concluded that the accuracy attained employing (n + 4)
equations is not worth the excess computer time required.
Typical soil surface temperatures obtained using 24 equations with 24 unknowns,
which are 60.9°F, 95.8°F, 128. 0°F, 136. 8°F, were modified as 61.2°F, 95.4°F, 126. 1°F,
134. 9°F, respectively, using the simplified method based upon Schmidt-Binder Technique.
On the other hand, the variation of computed air temperatures using either method has
been less significant.
564
Typical air outlet temperatures obtained by 24 equations have been 58.69°F,
69.88°F, 85.75°F, and 93.76°F; whereas, using 4 equations and Schmidt-Binder
Technique, respective temperatures have been 58.81°F, 69.82°F, 85.46°F, and 93.54°F.
4. Results of the Analysis and Experimental Verification
24-hour tests were run to verify the theories developed. The same experimental
data was used for a variety of computer programs and computed values were compared
with measurements as listed in Table III.
Table III - Comparison of Computed Values for Various Programs and Measurements
at Puerto Penasco on November 21, , 12 Noon
COMPUTER PROGRAM NUMBER
ITEM UNIT KUD03 KUD15 KUD21 KUD53 KUD61 KUD81 MEASURED
Ambient Temp. , DB
o p
70
. 8
Ambient Temp., WB
"f
63
.2
Air Inlet, DB
°F
85
.2
Air Inlet, WB
'f
84
.2
Air Outlet, DB
(200 ft)
°F
95
90
.16
91
.2
89
.7
88
2
89
.6
89
.0
Air Outlet, WB
(200 ft)
°F
87
86
8
86
. 8
88
86
, 5
Wind Velocity
mph
A
H
Air Velocity
ft hr-1
Solar Radiation Btu _
hr -^ft"^
208
Plastic Cover
Temp, at 50 '
°F
84
1
90
.16
87
09
81
5
83
.8
83
.7
Plant Temp. at 50 '
°F
93
6
85
9
86
03
89
8
86
1
86
8
87
. 4
Soil Temp. Surface
°F
111
9
102
2
107
8
92
4
100
3
95
1
97
. 5
Soil Temp. , 2"
*F
84
91
.4
88
.5
89
.9
Soil Temp. , 4"
*F
79
5
84
5
83
9
83
.4
Soil Temp. , 7"
"F
78
9
78
9
79
4
79
.4
Condensation on
the Cover
lb hr"-"-
25
9
53
.7
0) . lb
a, in
v/l^da
0
0
0
0
0
.
"a, in (200 ft)
v/^^da
0
0
0
0
0
.
The analysis with transpiration effects improves the computed leaf temperature
whereas considering evaporation from the soil allows to predict the soil surface
temperature more closely. The condensation rates could only be computed using the
program KUD81.
It should be noted that the analyses with no moisture effects and end effects were
developed for steady state operation; therefore, the typical radiation and ambient
conditions at noon were used to compare the computed temperatures. Soil temper-
atures below the surface are not available in the programs labeled KUD03, KUD15 and
KUD21.
The choice of program to be used depends upon the degree of accuracy desired, as
well as the cost of computation time. Typical computation times have been 8.954
seconds for KUD03, 13.968 seconds for KUD15, 16.816 seconds for KUD21, 26.599 seconds
for KUD53, 71.660 seconds for KUD61, and 51.058 seconds for KUD81 , on a CDC
computer.
565
The use of the advanced version of KUD 61 and 81 may be a drawback, especially in
case of using a low-speed computer.
5. Discussions and Conclusions
The prediction of temperatures and humidities in a controlled-environment green-
house enables the design engineer to maintain the temperature of air and leaf within
the safe and productive margins given by the horticulturalist .
Determination of the fan capacity, cooling or heating load where required, should
also be possible. The present mathematical formulation of the problem has proven to
represent the actual performance accurately enough for any engineering application,
since test results have agreed with the computer program.
The physical phenomena of transpiration, condensation effects on the plastic cover,
turbulence over the plant canopy, flow field through and around the canopies, penetra-
tion of solar radiation through plant communities have been separately treated by
investigators in various disciplines [7], [8], [9], [lO]. However, the results of
those surveys are not directly applicable to the specific system under study, since
they mostly consider each component separately. Physical properties of plastic cover,
plant and soil are not exactly the same as the present system. Besides, heat and
mass transfer coefficients must be determined for the surfaces under consideration.
Those studies would require sophisticated instruments and tedious experimentation
techniques while the present analysis aims to predict the overall performance of the
system rather than the detailed analysis of each component such as determination of
stomatal and boundary layer resistance of a single leaf.
The computer program developed however, is versatile enough to consider these
modifications on the analysis and in its present form, supplies the essential design
data on temperatures, humidities, and heating or cooling load.
Year-round performance prediction for the controlled-environment greenhouse has
been possible through the program KUD 91 which is virtually the same as KUD 81 except
the repeated number of runs and computer plotted curves.
A typical set of performance curves for the month of July at Puerto Penasco and
year-round variation of temperatures, humidities and condensation at 11:00 AM and
5:00 AM are sampled in Fig. 5) and Fig. 6) , respectively.
An extensive program is being launched by the Environmental Research Laboratory
of the University of Arizona, to investigate all those interrelated parameters in a
coordinated research effort. The findings of this survey should provide the most
accurate data for the prediction of the performance of an inflated plastic controlled
environment greenhouse.
Acknowledgements
The author wishes to express his thanks to Mr. Carl N. Hodges and the staff of
the Environmental Research Laboratory of the University of Arizona, for their help
during the different phases of the reseaich, especially the tedious experimental
program undertaken at Puerto Penasco, Mexico.
Dr. W. Gensler of the Electrical Engineering Department, deserves thanks for his
help in computer programming.
This work was carried out while the author was on leave of absence from the
Mechanical Engineering Department of the Middle East Technical University, Ankara,
Turkey .
Funds and equipment that were provided by the University of Arizona, the Abu Dhabi
Government, and the Rockefeller Foundation are gratefully acknowledged.
566
References
[1] HODGES, C.N. and HODGE, Carle 0.,
Power, Water and Food for Desert
Coasts, an integrated system for
providing them, 66 Annual meeting
Am. Soc. Hot. Sci . , Pullman,
Washington, .
[2] HODGES, C. N. and GROH, J.E.,
Controlled Environment Agriculture
for Coastal Desert Areas, 8th
National Plastics Conference, San
Diego, California, .
[3] HODGE, Carle O. , The Blooming Desert,
Bulletin of Atomic Scientists ,
Vol. XXV, No. 9, pp 32-33, .
[4] SELCUK, M.K., Heat and Mass Transfer
Studies of the Inflated Plastic
Greenhouses, unpublished report.
Environmental Research Laboratory,
University of Arizona, May .
[5] SELCUK, M.K. , Analysis , Design and
Performance Evaluation of Controlled
Environment Greenhouses , paper for
A.S.H.R.A.E. National Meeting,
June 29-30, , Kansas City.
[6] JACOB, M. , Heat Transfer, Vol. I,
pp 292-304, John Wiley, N.Y., .
[7] WALKER, J. N. and COTTER, D. J.,
Condensation and Resultant Humidity
in Greenhouses During Cold Weather,
Transactions A.S.A.E., pp .
[8] LEMON, E., Aerodynamic Studies of CO2
Exchange Between the Atmosphere and
the Plant, Harvesting the Sun,
pp 263-290, Academic Press, N.Y. .
[9] DECKER, W. L. Atmospheric Humidity
and the Energy Budget of Plant
Canopies, Jnl. Missouri Agr. Exp.
Station No. .
[10] COWAN, I. R., The Interception and
Absorption of Radiation in Plant
Stands, Jnl. App. Ecol. Vol 5,
pp 367-69, .
Nomenclature
D,p
d,p
pm
Area of plant receiving
direct radiation
Area of plant receiving
diffuse radiation
Ground area (Exposed to Solar
Radiation)
Area of plant (convection H.T.)
Area of plant (Radiation H.T.)
Area of the cross section
Thermal diffusivity (soil)
Specific heat of dry air
Specific heat of moist air
Specific heat of soil
UNIT
ft^
ft^
ft^
ft^
ft^
ft^
ft' hr"i
Btu lb~^
Btu lb~^
Btu lb~^
FORTRAN
NOTATION
ADIRP
ADIFP
AGROU
AP
APR
CROSEC
THDIF
CEAIR
CESO
Radiation Heat Transfer Shape
factor
3- = F ' e Radiation H.T.
Shape Emissivity Factor
Dimensionless
Dimensionless
567
p,c
(F ' e ^ ' e ^ ) Radi-
p , c p , Lw c , Lw
ation heat transfer between
plant and cover
s , c
e T * e T ) Radi-
s,Lw c,Lw
s ,p
s , c
ation heat transfer between soil
and cover
(F ■ e T ' e T ) Radi-
s,p s,Lw p,Lw
ation heat transfer between soil
and plant
Enthalpy of dry air
Enthalpy of saturated liquid
Enthalpy of phase change, evapora-
tion
Enthalpy of saturated vapor
interf Enthalpy of air stream at
the plant interface
he.
1
he
he
he
Convective H.T. inside
Conveetive H.T. over plants
Convective H.T. over soil
Conveetive H.T. due to wind
w
hr , ERHTC - cover to sky
C / SK
hr , ERHTC - plant to sky
P / SK
hr , ERHTC - soil to sky
s,sk ^
ERHTC - plant to cover
ERHTC - soil to cover
ERHTC - soil to plane
hr
p,c
hr
hr
I
s ,p
Solar radiation intensity
Direct solar radiation intensity
Diffuse solar radiation intensity
Mass Diffusion coefficient
Mass Diffusion coefficient at
cover (Condensation Rate)
Mass Diffusion coefficient at
plant (Transpiration)
UNIT
Dimensionless
Dimensionless
Dimensionless
Btu lb
Btu lb
Btu lb
Btu lb
Btu lb
_ 1 _ 2 o _ 1
Btu hr ft F
1 2
Btu hr ft
_ 1 2
lb hr ft
FORTRAN
NOTATION
FRPC
FRSC
FRSP
HDA
HF
HFG
HG
HCIN
HCPL
HCSP
HWIN
HRCOSK
HRPLSK
HRSOSK
HRPC
HRSC
HRSP
RADI
RADIR
RADIF
OKC
OKP
568
■ bar
■ v,a
V, m
T.
1
stom
db
wb
"sky
■ 1 , in
" 1 , in
Mass Diffusion coefficient over
soil (Evaporation)
Thermal Conductivity
Soil Thermal Conductivity
Mass Flow Rate of air
Perimeter : n ' R
Partial pressure of air
Barometric pressure
Total (mixture) pressure
Partial pressure of water vapor
Partial pressure of water vapor
at ambient air
Partial pressure of water vapor
initially
Total heat transferred
Heat transfer rate
Greenhouse cross section radius
Stomatal resistance to mass
diffusion
Time
Temperature
Temperature of air inside the
greenhouse
Ambient Air temperature
Dry bulb temperature
Wet bulb temperature
Equivalent sky temperature
Initial temperature (Dry Bulb)
(Wet Bulb)
Volume flow rate
Velocity
Wind velocity
UNIT
lb hr ft
_ 1 _ 1 _ 1
Btu hr ft °F
lb hr
ft
psia
psia
psia
psia
psia
psia
_ 1
Btu hr
_ 1 2
Btu hr ft
ft
_ 2 _ 1
hr ft lb
hrs
°F
°F
°F
Op
°F
°F
°F
3 1
ft ft"
FORTRAN
NOTATION
OKS
CONSO
PERIM
PBAR
PMIX
PVAM
PVI
RADIUS
RSTOM
TIME
TEAIR
TAM
ft hr
mph
TSKY
TINIDB
TINIWB
VEL
WIND
569
c , sw
C ,Lw
a
p,sw
p,Lw
s , sw
s ,Lw
p,sw,D
p , sw , d
'c ,Lw
'p , Lw
's ,Lw
c,Lw
T
c , sw
Ax
At
Nomenclature
Greek Symbols
UNIT
Absorptivity, cover shortwave Dimensionless
Absorptivity, cover longwave Dimensionless
Absorptivity, plant
Absorptivity, plant shortwave
Absorptivity, plant longwave
Absorptivity, soil shortwave
Absorptivity, soil longwave
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Dimensionless
Absorptivity, plant shortwave, Dimensionless
direct radiation
Absorptivity, plant shortwave, Dimensionless
diffuse radiation
Emissivity, cover longwave Dimensionless
Emissivity, plant longwave Dimensionless
Emissivity, soil longwave Dimensionless
Cover, transmissivity Dimensionless
Cover, transmissivity longwave Dimensionless
Cover, transmissivity shortwave Dimensionless
Thickness of the soil slab
e. . ,
init
Space interval (Length of the
System)
Time Interval
Humidity ratio
Humidity ratio of air
Initial humidity ratio
Humidity ratio of saturated
air, at the cover temp.
Humidity ratio of saturated
air at plant temp.
Humidity ratio of saturated
air, at soil surface temp.
Relative humidity of air
initially
ft
ft
hr
lb /lb ,
V da
Dimensionless
FORTRAN
NOTATION
ALFCSW
ALFCLW
ALFPSW
ALFPLW
ALFSSW
ALFSLW
AFPSWR
AFPSWF
EMCLW
EMPLLW
EMSOLW
TRAN
TAUCLW
TAUCSW
DELSO
DELX
DELTIM
OMEGA I
OMEGIN
OMEGCO
OMEGPL
OMEGSO
PHIN
570
si
s2
Transparent cover temp.
Plant temperature
Soil surface temperature
Soil temperature 1st slab
Soil temperature 2nd slab
Soil temperature 3rd slab
Soil temperature kth slab
Density of dry air
Density of moist air
Density of the soil
UNIT
°F
°F
°F
°F
°F
°F
°F
lb ft
m
FORTRAN
NOTATION
TECOV
TEPLA
TESOI
TSl
TS2
TS3
ROAIR
ROMAIR
ROSO
a
am
c
D
d
da
db
i
Subscripts
air
ambient
cover
Diffusion, Direct for solar radiation
diffuse, solar radiation
dry air
dry bulb
inlet, inside
init.,in initial
interf. interface
Lw longwave
m moist air
o outlet, outside
p plant
s soil
sat saturation
sk sky
sw shortwave
V Vapor
w water
wb wet bulb
571
572
573
'READ
DATA
PROR
CALCULATE
MOIST AIR
PROPERT
101
A: MATRiX
CiMATRiy"
CALL
COZUM
(a>-
PART PRES.
AIR AT
PLANT TEM
401
E: MATRIX
G: MATRIX
TECOV(M)CI
TEAIR(M)C2
TEPLNW C3
TES0L(M)C4
4 SI MULT
EQUATIONS
NO-MOIST
SOLUTION
SIMULTAN.
EQUATIONS
GAUSS-JOR.
4SIMULT
EQUATIONS
W/TRANS.
ONLY
SOLUTION
OF SI MULT
EQUATIONS
GAUSS-JOR.
A^p ERROR
ERR.=TEPL
NW-TEPLA
NEWTON-
RHAPSON
APPROX.
64
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588
Computer-aided System
for
Preliminary Air Conditioning Design
E. Maki and Y. Okuda ^
Nikken Sekkei Komu Co. , Ltd.
Mechanical Department
Japan
In preliminary designing stage of air conditioning system, there is a time
when the information necessary for deciding the zoning, type of system, gen-
eral layout, types of equipment, cost, etc. must be obtained by preparing a
schematic design of the proposed system to see if it will meet the basic design
requirements. The information thus obtained may be fed back to those con-
cerned so that they can make necessary project coordination. In order to
make it possible to deal with the work required at such stage effectively by
utilizing a computer, the authors developed a system titled COSMA which was
intended for continuous processing of heat load computation, equipment selec-
tion, pipe and duct designing, etc. Based on the experienced gained through
its trial use, COSMA is now being reorganized into SPACE (Subprogram and
Phrase for Air Conditioning Engineers) which is featured by the following
characteristics:
1. A variety of subprograms and files is available so as to enable the selection
of various equipment, basic design of ductwork and piping work, cost esti-
mating of principal elements, etc. on the basis of heat loads.
2. The system is flexible and allows free combinations of phrases in accord-
ance with thinking sequence of the designers.
3. Simplified input data are another feature of this system.
4. The system is composed of subprograms which are minutely divided into
fxmctional units by well documented and classified files. These subpro-
grams and files are designed to be easily expanded, modified or adapted to
cope with varied conditions. Moreover, considerations have been given
so that they can, in future, be coupled with the computer-aided systems for
other engineering areas such as electrical, plxombing, architectural and
structural.
This system enables the designers to obtain the basic data which are more con-
crete and objective in a shorter time, and thus makes it possible to study more
alternatives within the given time.
Key Words: Preliminary air conditioning design, computer-aided system,
equipment selection program, duct design program, pipe design program,
AC system design program.
echanical Engineers
589
1. Need of Developing a Computer Program
for Preliminary Design
At an early stage of architectural planning, an air conditioning engineer must propose a prelimi-
nary air conditioning design which will satisfy the given conditions. At this stage, he must make
necessary investigations and propose a creative design based on his professional intuition and experi-
ence. Then, he must check to what extent the aforesaid proposal will satisfy the given conditions,
decide whether the proposal shoiild be adopted, and, if it is to be adopted, determine the optimum
scope of the system. If not, he will have to make some alternative proposal, or request the architect
to restudy and modify the architectural design, or in some cases, he will have to ask to modify the
basic design conditions and requirements in conformity to which he has prepared the original proposal.
The data required at this stage will include: (1) the initial instUation cost; (2) the operating cost;
(3) the physical size of each element of the system to give the basis for coordinating the relation of
architectural and structural designs with the air conditioning design; (4) the data indicating the antici-
pated ambient conditions (including the values, changes and distribution of temperature, humidity, air
flow, etc. in each room and parts thereof) which will be created by the proposed system. The data
is important because they will enable the mechanical engineer to foresee if these conditions meet the
design requirements.
The data described above need be prepared and evaluated by two methods: in the method (A), the
evaluation of the data (1), (2) and (3) will be made through a statistic approach, namely on the basis of
analyses of assembled data, while the data (4) will be assessed on the basis of professional experience;
and in the method (B), the data (1), (2) and (3) will be obtained by the schematic design studies of the
proposed system and the data (4), by means of simulation. (It should be noted that the methods (A)
and (B) are mutually supplementary, and one is not enough without the other to insure an accurate and
proper determination. )
It, however, may be generalized that the method (B) is more direct and convenient in seeing
quantitative differences beween a number of proposed systems with respect to the data (1), (2) and (3).
Since a considerable part of the work required at this stage can be systematically structured, a
utilization of a computer at this stage should enable a mechanical designer to evaluate a larger num-
ber of alternative proposals in a comparatively short time, and this should make it possible to make
feed-backs to the architect and the owner in a more effective manner. For this reason, the develop-
ment of a computer-aided system for the aforesaid schematic design studies is highly desirable.
The firm of Nikken Sekkei took to the development of such a computered system in , and
completed the first edition of the program in . Based on the experience in using this program,
the firm began to revise the program at the end of . In the following paragraphs, the authors
intend to describe briefly the first edition of the program, the advantages derived from it, the reasons
why the first edition had to be revised, and the concept and present status of the new system now in
the course of development.
2. Program Group for Schematic Designs
COSMA - First Edition
2. 1. General Description
The scope of COSMA First Edition is as shown in figures 1 and 2 and the program has been in use
at Nikken on some of the actual project on a trial basis.
Basically, COSMA is composed of the following three groups of programs:
(1) Programs for a continuous data processing from heat load computation to selection of various
equipment.
590
(2) Programs for designing duct and piping systems
(3) Programs which, for some typical perimeter zone and interior zone systems often adopted in
practice, enable a continuous data processing, by means of simplified input data, for all design
stages such as heat load computation, selection of terminal \anits, pipe and duct design and cost
estimation.
(1) Outline and features of program for heat load computations
and equipment selections
The first step in a series of processes described in this paragraph is to define space \mits and
zones in the building for the purpose of planning. The word "space-unit" may be defined as a minimum
unit of space which is used as a basis for the load computation. The term "zone" as used here de-
notes a building space which is regarded as a minimum independent area in air conditioning planning,
and zones are classified depending on their load characteristics and the intended purposes. Each
zone is defined as a group of space units. The program to be discribed later in this paragraph use
the aforesaid unit space and zone as a basis. The program is capable of dealing with up to 36 types
of space units and 60 zones for one building.
The second step is to make heat load computations to give a basic data for the entire air condi-
tioning system design which includes the selection of equipment and the designing of ducts and piping.
The program introduced here is so contrived as to enable numerous detailed computations required for
large buildings with well-organized simple input data. The computation according to this program
follow the steps mentioned below: (1) data for calculation for the various types of interior are fed to the
computer, each input data card representing one type; (2) next, various combinations of the perimeter
and the interior types and requirements for fresh air intake are fed for each space unit with two cards
per space \mit. Based on the foregoing input data, the computer calculates the heat loads for all
space units and then sums them up to give the heat load for each zone. The zonal heat loads are fur-
ther summed up to give the heat load for the whole building. Then, as the last step in heat load
computation, flow rates of air, chilled and hot water, steam and other media are computed for each
zone.
The third step in this program is for the user to assign a group of chillers, boilers, p\imps, air
conditioners, etc. to each zone according to the air conditioning system under consideration. Each
group of chillers etc. is given an identification niimber; and the zone or zones to be served by the res-
pective group are indicated by the aforesaid identification number. Also, the nxomber of equipment
needed for each group is determined.
The input data are given in the form of cards, one card being provided for each zone. The niim-
ber given at the equipment type coliimn on each card indicates the identification number of the set of
equipment which takes care of the zone the card represents. The number of equipment for each group
is indicated on the same card. A pump may be designated to handle chilled water, hot water or con-
denser water to meet seasonal requirement. Thus, if the chilled water pump column and hot water
pump column of the card are given the same number, it means that a single pump is to handle both
chilled water and hot water.
The fourth step is to select equipment on the basis of the heat loads, flow rates and system de-
signations obtained in the previous step. At this stage, such requirements as types of apparatus are
also specified on the input data. The data necessary for specifying such requirements can be taken
from the information supplied by the manufacturers, arranged and stored on disks.
The output data give the information on the type, performance, size, weight, cost, etc. of each
equipment. For some kinds of equipment, this information is given in the form of a comparative
table showing performance etc. of various makes and models.
591
Sampl
e input data showing zone-equipment-system relations (Simplified for
explanatory purposes)
Zone
Chiller Boiler
Pump
Air
Condenser Primary Secondary
Hot
Conditioner
Water Chilled Chilled
Water
Water Water
1
1 1 1
4 7
1
1
2
1 1 1
4 8
1
2
3
1 1 1
4 9
1
3
4
2 1 2
5 5
10
4
■ 5
2 1 2
5 5
10
5
6
2 1 2
5 5
10
6
7
3 1 3
6 6
6
7
The meaning of the above input data is:
No. 1
chiller is for Zones No. 1, No. 2 and No. 3.
No. 1
boiler is for all zones.
No. 1
pump is for condenser water and hot water fo
r Zones No. 1 , No. 2 and No. 3.
No. 2
pump is for condenser water for Zones No. 4,
No. 5 and No. 6.
No. 6
pump is for primary- secondary chilled water
and hot water for Zone
No. 7.
(2) Outline and features of piping and duct programs
In the piping program, the locations of equipment, the required flow rates of water, the desired
flow resistance, etc. are fed as input data, according to which the computer calculates the appropriate
pipe diameters at respective sections of pipeline, and gives the pipe sizes, flow resistance, lengths
which are useful for cost estimation, etc. Pipe sizes are determined to equalize the resistances of
all branches. Input data are prepared by nodal description method. In the duct program, the design,
cost estimate, outlet and mixing box selection, etc. are processed on the basis of input data which are
prepared by nodal description method.
(3) Outline and features of the programs for AC system
The flow chart in figure 2 indicates what can be processed by this set of programs. In com-
puterizing the process of obtaining necessary information through schematic designs of a fan-coil unit,
an induction unit, a dual-duct or a single duct system, the greatest difficulty is usually enco\mtered in
how to computerize the designing of duct and piping systems. This difficulty results from the fact
that the input data become, more often than not, highly complicated in proportion with the importance
of the information. To avoid this diffic\ilty, the nodal description method is dispensed with in pre-
paring input data for duct and piping design as shown in figures 4 and 5.
Instead, a set of input sheets into which an architectural modular grid is entered in the form of
matrices based on the elevations and plans is used. On these input sheets, the designer writes either
in symbols or in numerals, the designations as to the following: (1) the types of systems to be studied
(the name of systems and designation of the number of pipes, i. e. , 2-pipe, 4-pipe, etc. ); (2) the type
designation of duct and piping system; (3) the type of piping (reverse-return etc. ); the data necessary
for computations (computation method, friction loss per unit length, etc. ). The program is formu-
lated in such a way that heat load computation, selection of terminal units, and further duct and pipe
computations and cost estimating can be performed by a computer. As shown in figure 3 , these
program requires only two input data sheets to study up to three different perimeter systems.
592
(4) Scope of the program
No. of Main
No. of Sub-
Steps
Fixed Data
Programs
Programs
(Sectors )
Psychrometirc Chart
0
18
300
Heat Calculation and Flow Rate
8
1, 000
35
Equipment Selection
38
9
5, 000
715
Perimeter System
1
8
3, 500
23
Interior System
1
9
3, 000
28
Piping
1
1
500
1
Ductwork
2
7
2, 000
10
Altogether, these amount to one and one half disks in area.
2. 2. COSMA promoted design efficiency
The authors utilized COSMA when they designed the air conditioning system for a 20- storied
building having a floor area of about 10, 000 sq. m or 106, 500 sq ft. In this case, the computer
(IBM ) was used to process those data which are shown above the dotted line in figure 1 , or in
other words, the data concerned with the steps from the heat load computation to the equipment
selection and study. The relevant information desired by the designers was obtained in less than five
hours, the designers spending two to three hours for input data preparation and the computer personnel
spending about two hours for pimching, running, etc.
Also, COSMA was utilized in designing the air conditioning system for another 20-storied build-
ing with a floor area of some 30, 000 sq. m (318, 000 sq ft). In this case, it was assumed that the
whole system was composed of 8 perimeter systems and 12 interior systems, and three alternative
system types (induction unit system, fan coil system and dual duct system) for the perimeter and also
three system types (single duct system, dual duct system and individual zone system) for the interior
were considered. It took about 8 hours for input data preparation, 3 hours and 15 minutes for com-
puter processing, and another 8 hours for manual assorting and editing of the output data.
From these experiences, it was learned that all the data processing for COSMA System could be
done in one day if the output data were limited to the point of equipment studies, and in about three or
four days if the output data were to include those concerning duct and piping designs and comparison
of alternatives. With the efficiency thus achieved, the system was considered capable of serving the
intended purpose satisfactorily.
2. 3. Some problems with COSMA
After having been used for the past year on a trial basis by some machinery engineers of our
firm, it is considered that COSMA should be improved with respect to the following:
a. COSMA consists of a niimber of subsystems; however, it is rather strongly characterised by its
being one inseparable system. This character of the system makes it difficult to pick out and com-
bine desired programs freely as the occasion demands.
b. The need is felt that the system should allow for a greater freedom in setting up the most desirable
flow of data processing for each individual project.
c. COSMA is capable of dealing with the air conditioning systems generally used at present. The im-
provement of the system to make it easily adaptable to new design situations, such as the
development of new equipment or unique air conditioning system combinations, is considered nece-
ssary.
d. It is desired that COSMA have a means of output control so that the computer can give the specific
information reqmred at any given phase of the data processing,
e. It is desired that COSMA be made capable of aiding the design work from the earlier stage of design
than is possible with the present program.
3. Development an Assembly of Phrases for Schematic Designs
- Development of SPACE (Subprograms & Phrases for Air
Conditioning Engineers)
3. 1. Two approaches to the development
There appear to be two approaches to arrive at the solutions for the problems described in the
paragraph 2. 4. , with the original system being used as basis of the further development.
(1) Developing a group of approximation formulas
In one way of approaching the solutions, the whole group of programs is regarded as a data gen-
erating system, with the conditions given to COSMA being changed systematically. The resxilting
output data can be handled and organized as in the case of statistic data. Then, a variety of approxi-
mation formulas can be obtained for these output data, and this group of formulas can be converted
into programs to obtain important information.
(2) Subprograms and phrases
Another approach to the improvement of original COSMA is to decompose it into as many minute
mono-functional subprograms as possible and, at the same time, to standardize all the files.
These subprograms and files can then be organized as required by application of IBM-plan tech-
nique (1) ^ into a set of phrases for air conditioning designs. It is expected that this process can
eliminate the drawbacks of original COSMA to a large extent without losing its features.
The air conditioning designers who use this system (SPACE) are not supposed to look at the input
data sheets and make entries for the necessary items disregarding the inapplicable optionals, all ac-
cording to the designated processing sequence. Instead, the designers are requested to arrange the
phrases and data as necessary for the designs, so that they can use the program in a more flexible
and versatile manner. The system as has been developed to date is as outlined in the following para-
graphs.
3. 2. General setup of SPACE
Figure in parenthesis indicates the literature referenced at the end of this paper.
594
(1) Outline of the system
Subprograms:
At present, our primary efforts are being directed to dividing COSMA subroutines into as mi-
nutely classified subprograms as possible and setting up appropriate output controls which precede
output instructions. The number and scope of such programs, therefore, can be surmised by refer-
ence to the scope of COSMA described in the section 2 of this paper.
File group:
The files are generally organized as follows:
(i) Common data files - These files contain the data applicable to all kinds of projects.
(ii) Project files - For these files, only the framework of data storage system (the name of file,
the sequence of data filing, etc. ) is predetermined, so the designer must compile a file for
each individual project by using the applicable phrases.
The major files of each category will be described in Appendix A.
Phrases:
Presently, the COSMA subprograms which have been decomposed are being reorganized into a
set of new phrases. The composed phrases will serve the purpose of primary operations. As the
next step, the need is felt to develop the phrases which can be used for secondary operations. These
phrases for secondary operations should be capable of modifying a part, not all, of the input data given
out in primary operations, and of reprocessing the phrases which have been modified. For instance,
such a phrase may read "SELECT CHILLERS FOR CHANGED CONDITIONS, "
(2) Relationship between subprograms and phrases
Since it is apparently impossible to describe the computered design process for an entire air
conditioning system within the space allowable for this paper, the functions of subprograms and the
subprogram-phrase relationships will be described for some of the phrases used in perimeter system
designs. The function of individual subprograms will be further described in Appendix B.
ALC-33 Instructions to read the project titles etc.
ALC-34 Instructions to read the design climatic conditions
LAC-44 Instructions to compute heat loads
AAV-44 Air volume computation
AOAV 1 Designation of primary air
AFCO 2 Selection of fan coils
AZON 3 Subprogram for defining the zoning by matrix
APMO 1 Piping design for unit space expressed by matrix
ADMO 1 Duct design for unit spaces expressed by matrix
(a) Some examples of phrase usage
The design can be worked out by a variety of methods by utilizing the foregoing subprograms as
shown by the following examples. (The subprograms listed in parentheses are shown for explanation
only, and are necessary only for defining the phrases.) In actual use for a specific project, phrases
and data only need be stated.
On the outset of a project, the heat computation is conducted:
LOAD CALC BY ALC : (ALC-33, ALC-34 & ALC-44)
At the next step, the phrases such as the following may ensue:
595
(1) SELECT FAN COIL (AFCO 2):
The instructions that proper fan coil units be selected for each space unit.
(2) SELECT FAN COIL WITH PA (AOAV 1 and AFCO 2):
The instructions that proper fan coil units be selected against the load differencial computed by-
deducting the cooling capacity of the primary air supplied to each unit space according to the ,
applicable criterion from the loads on space units.
(3) ZONING BY MATRIX; ZONE (AZON 5)
DESIGN FAN COIL SYSTEM (AFCO 2 APMO 1)
By these phrases, a computer is instructed to select fan coils and execute piping design and cost
estimating on the basis of the given data indicating the proposed space xmit layout and piping sys-
tem.
(4) ZONING BY MATRIX; ZONE (AZON 5)
DESIGN FAN COIL SYSTEM WITH PA (AOAV 1, AFCO 2, APMO 1 and ADMO 1)
After the primary air supply data have been fed and fan coil units have been selected as described
in (2), the piping for fan coil units and the ductwork for primary air are designed and estimated
by the instructions phrased as above. In this example, space unit layout only has been instrut-
ed by ZONING phrase, and separate instructions as to how the pipes and ducts sho\ild be laid out
must be given by the imput data included in APMO 1 and ADMO 1. Therefore, no trouble will
ensue even if the duct layout differs from the piping layout.
For single duct and other systems, the phrases may be combined generally in the same manner
as described above.
4, Conclusion - Versatility of SPACE System
The authors wish to conclude this paper with a brief statement on the development potentiality
of this system.
i. The input data for this system can be further simplified by unifying them with the files for other
engineering disciplines. If the physical data on space xmits are included in the files prepared
by architects, structural engineers or cost estimators, the physical data necessary for heat
load computations can be taken from such files.
ii. The system is adaptable to the future development of equipment. For instance, if it is assumed
that a new type of equipment is developed for air and water system or for water system, and that
the equipment is named XUNIT and a new program named XPROG is developed for selecting
this equipment (such a program should be developed without difficiilty because it is to serve a
simple purpose of selecting a type of equipment and computing water and air flow rates), the
phrases to be used for the design of the system wherein such new equipment is used can be com-
pleted simply by replacing the word FANCOIL in the phrases (1) - (4) with the words XUNIT and
by using the word XPROG in lieu of AFCO 2 in the program list.
iii The system has high adaptability to a variety of system combinations.
iv The system has an advantage in that, in developing programs, subprograms may be developed by
an engineer or a programmer, and the phrases can be developed by someone else who system-
atizes that subprogram.
5. References
(1) IBM, Program language analyzer (Plan), Program description manual, January
596
6. Appendix
Appendix A Structure of files
(1) Common Data Files
a. Foundamental data file consisting of basic data on climatic conditions, physical properties,
etc.
b. Catalogue data file consisting of the data on equipment performance, sizes, cost, etc. which
have been taken for storage from trade literature.
c. Statistic data file (Data to be stored in future)
d. Standard data file (Data to be stored in future)
(2) Project Files
a. Physical data files concerning space units:
The data in these files shows the shape, dimensions (length, width and height), and other
physical data on space unit as a shell.
b. Air conditioning system files:
These files contains the information relating to the zoning and system designations.
c. Equipment data files:
d. Heat load files:
The results of heat load computation and the loads as determined from the required fresh
air volume are filed.
e. Air data files:
These contain the data relating to the air volume, primary air volume, pressure loss, etc.
for each space unit.
f. Water data files:
Water flow rate, head loss, etc. for each space unit are filed.
g. Files of data on selected equipment:
The framework to be determined in future.
Appendix B Description of subprograms
ALC-33
ALC-34
ALC-44
AAV -44
AOAV 1
This subprogram instructs a computer to read the title of project, the names of designers,
the data the design was executed, etc.
This instructs a computer to read such design conditions as the temperature and humidity
of outside and room air, and the shadow factors. ( — > Design conditions and — > shadow
factors files )
This instructs a computer to read the data on each space unit ( -*■ Space unit file), to com-
pute the area, volume, etc. ( -» Physical data file for space unit), and to compute heat
loads ( Heat data files). Where the zoning is defined at this stage, the zoning infor-
mation is also stored in the appropriate file ( -* System file).
The name of zone for which computation is to be made; the computation method((^T^by ADP,
(^T) by the predetermined temperature difference of supply air, by the number of air
changes, ^^by the air volume per unit area, or(^T)by the predetermined air volume per
person in tlie unit space), and the criteria for fresh air volume ( (T^ per area, (^Z^per
person, (^i^per air change, or (^4^ by percentage of the total air supply) are to be instructed.
On the basis of these instructions, a computer will, by reference to Heat data files, calcu-
late air volume ( -» Air data files), fresh air volume ( — » Fresh air data files), the
conditions at coil inlets and outlets ( -> Coil data files) for both summer and winter and
will store all these data in the appropriate files.
In accordance with the supply requirements (per area, per person or on the basis of desig-
nated value) provided for each unit space within a designated zone, this subprogram
597
instructs a computer; to calc\ilate, making reference to the data on area, number of per-
sons, etc. in architectural file, the primary supply air volume ( Primary air files); to
compute the cooling or heating capacity of primary air under the given supply conditions
( -> Coil files, with the design outside air data being filed also in Coil files as the coil inlet
conditions); and to compute the coil loads ( Coil files).
AFCO 2 This subprogram instructs a computer to select appropriate fan coil units for each unit
space within the zone under consideration, making reference to Heat files, and also to
Cooling and Heating capacity files if so instructed (Type, number, water flow rate, pres-
sure loss of the units to be filed in Water files).
AZON 3 This subprogram instructs a computer to transform the simplified space unit arrange-
ment given in the form of a matrix into a perfect arrangement and produce it as output.
( -> Zoning files)
APMO 1 Where unit space arrangements are shown by matrices, this subprogram instructs a com-
puter: to determine the flow rate, diameter and flow velocity for each branch line according
to such input data as the piping layout pattern numbers, the designation as to the loop-
reverse, design friction head loss, etc. ; ajid further to obtain the total head loss { Water
files) and the pipe lengths by the diameter. ( Material files)
ADMO 1 This subprogram is basically same as APMO 1.
598
Heat load calculation
Air volume, water flow rate
&: steam flow rate calculation
Equipment selection & cost estimation
Central ref. machine
Absorption ref. machine
Cooling tower
Boiler & pump
Fan
Packaged air conditioner
Air handling unit
Air filter
Fan coil unit
Induction unit
Piping design
and
estimation
Duct design
and
estimation
Fig. 1
The scope of COSMA
599
Read the data showing
the architectural configu-
ration of each space-unit
Compute the load for each
space-tuiit (for summer,
fall and winter)
X
Read wall arrangement,
the system to be studied,
and the other necessary data
Fan coil sysbem
Single or dual duct systems
Induction unit systems
Select fan coil unit and
dtermine required flow
rate of water
Design pipelines
(Compute flow rates in
various parts and deter-
mine pipe sizes
Compute the required
flow rate of supply air
>
Select diffusers and
blending units
1
' -1
Select induction units and
compute the required flow
rate of water and primary
air
Compute the quantity
of piping materials
Design Ductwork
(Compute air flow rates
in various parts and de-
termine duct sizes)
Compute the quantity
of terminal units
Design piping systems
(Compute the flow rates in
various parts and determine
pipe sizes)
Compute the quantity of
sheets metal or spiral ducts
by the metal thickness or
the diameter
Design duct systems
(Compute the air flow rates
in various parts and deter-
mine duct sizes)
I
Compute the quantity of
terminal \inits, the quan-
tity of pipes by the size
and the quantity of sheet
metal thickness or the
diameter
Fig. 2
Flow chart for perimeter system program
600
^rri^rnTiij
Entire
elevation
li "
i
— r
' —
[!
1
1
m
3rlH
South elevation
A
Unit number
B
Floor-ceiling height
C
Window glass area ratio
Entire
D
Window orientation
input
E
Heat transmission coefficient for glass
data
F
Shadow factor
G
Grade of heat storage
H
Shade factor
I
Heat transmission coefficient for wall
J
Equivalent temperature difference
K
Area of other walls
L
Orientation of other walls
M
Heat transmission coefficient of
other walls
N
Equivalent temperature difference
O
SH due to causes other than humans
&r Lighting
P
LH due to causes other than humans
& Lighting
Q
Load factor for interior loads
R
No, of occupants in a unit
S
W per sq. m
Fig. 3 Input data arrangement (for perimeter system
study program)
601
Sheet A
Module combination
(copied from the elevation)
Quasi-nodal description is
automatically produced.
Sheet B
-f-
Selection from
duct & pipeline
prototypes
Ducts and pipings
computed and estimated
Selection of
piping systems
Fig. 4 Schematic chart showing the duct and piping
data processing procedures (for perimeter
system program)
602
Computer selection and evaluation
of Design Weather Data
E.N. van Deventer
Environmental Engineering Division
National Building Research Institute
CSIR Pretoria
The need for hourly design weather data, particularly in
climatic situations typified by large diurnal variations in the
individual elements, is stressed.
For the purpose of determining design data, typically hot
days are first selected on the basis of either computed daily
maximum sol-air temperatures or daily maximum dry-bulb temperature
occurring on 10 per cent, 5 per cent and 2.5 per cent of the
occasions for the period under consideration. Typically cold days,
on the other hand are selected on the basis of daily minimum
temperatures occurring for the same percentages of the time.
The design data are evaluated from coincident values of the
four elements, viz. dry-bulb temperature, humidity, wind and
solar radiation, as they actually occur in practice.
The foregoing is accomplished by the following Fortran IV
computer programmes:
SELECT - This programme computes daily maximum sol-air
temperature, threshold daily maximum sol-air temperatures. It
lists the year and day of year on which the daily maximum sol-
air temperature equals or exceeds the threshold values. In
addition it computes hourly values of Linke turbidity factor and
precipitable water vapour content of the atmosphere.
SOLAR - This programme computes hourly values of direct
solar radiation, diffuse solar radiation and atmospheric trans-
mission coefficient for clear sky conditions for places for which
such information is not available, from estimated hourly values
of turbidity coefficient and solar constant.
DWDATA - This programme computes design weather data
selected by programme SELECT, OR, from hot days selected on
the basis of daily maximum dry-bulb temperature, OR, from cold
days selected on the basis of daily minimum dry-bulb temperature.
The solar radiation information is computed for horizontal as well
as vertical surfaces.
Key Words: Weather data, design, computer, computer pro-
grammes, FORTRAN, thermal performance, buildings, Sol-air
temperature, Linke turbidity factor.
*
Senior Chief Research Officer.
603
1. Introduction
The climate over the major portion of Southern Africa can generally be
described as warm and dry. Such climates are usually typified by large diurnal
variations in air temperature, high solar radiation intensities and an abundance of
sunshine. For instance, the mean annual duration of sunshine for the western in-
terior of South Africa is more than 80 per cent of the maximum possible duration,
whilst over the coastal areas it rarely falls below 60 per cent except along the
west coast where 50 per cent is a more likely value. (l) Under such circumstances
th® outside surface of the exposed elements of a building are alternately heated
strongly during the day and cooled strongly at night so that there is a marked
periodic flow of heat in and out of such elements.
2. Selection of Weather Data
Design weather data for evaluating the thermal performance of buildings
subjected to periodically fluctuating heat flow conditions must be given on at least
an hourly basis. Furthermore any method of selecting weather data from which design
information is to be evaluated should be aimed at describing the weather on typical-
ly hot days in summer and typically cold days in winter. Defining a hot or cold day
with respect to the thermal performance of buildings, however, is still a matter of
speculation, although computed daily maximum sol-air temperature seems "co offer the
best possibility.
Winter design data should obviously be based on weather conditions that induce
the maximum cooling of a structure. Under South African conditions, days with the
lowest minimum temperature would represent such conditions in the interior, since,
generally speaking, these low temperatures are due to high rates of radiative cool-
ing during the night. However, in certain areas, such as the South-Western Cape,
maximum cooling rates are usually experienced during the passage of a cold front
with accompanying high winds and low temperatures.
More specifically, the selection of weather data for design purposes is more
usefully made in accordance with the probability that similar or worse weather con-
ditions will occur on as relatively few occasions during the summer and winter as
will justify the specific design criteria; the data should therefore be selected
from coincident values of the pertinent weather elements as they actually occur in
practice and should be expressed in terms of the diurnal variation of the elements.
Runs of successive days of hot or cold weather of different duration must also be
evaluat ed . ( 2 , 3 , 4 )
Five years of hourly air temperature, relative humidity, wind and solar
radiation data for 15 places in South Africa, South West Africa and Botswana, have
been selected for analysis in this way. It is envisaged that the number of stations
for inclusion in this study will be significantly increased shortly.
The principles outlined above have been used in the preparation of computer
programmes for selecting weather data and evaluating design weather conditions for
the thermal performance assessment of buildings. The programmes are written in
FORTRAN IV for implementation on an IBM S/360 model 65 IH operating under Operating
System Release 18 MVT (Multiprogramming with Variable number of Tasks). The
package consists of three main programmes, viz SELECT, SOLAR and DWDATA and sixteen
subroutine sub-programmes.
3. Description of Computer Programmes
3.1 SELECT
The thermal interaction between a building surface and its immediate micro-
meteorological environment is a function of the integration, in some way, of the
relevant meteorological parameters . (5 ) The concept of sol-air temperature, intro-
duced by Mackey and Wright (6) provides such an integrated meteorological parameter.
It therefore seems reasonable to select simmer design weather data on the basis of
sol-air temperature. For purposes of comparison, however, days are also selected
purely on the basis of maximum dry bulb temperature.
(l) Figures in brackets indicate the literature references at the end of
this paper.
604
Sol-air temperature may be expressed as follows: (7)
5 = Q +
sa oa
s - -^It
hnr.
(1)
where 9 is the sol-air temperature, Oga "the dry-bulb temperature, oC the
absorptivity of surface for solar radiation, Ig the Intensity of solar radiation,
the long-wave radiation balance of the surface and hoc the coefficient of
convective heat transfer between the surface and the air.
The outside convection coefficient and low-temperature radiation exchange of
the surface and its surroundings are not generally known and the values for both
these factors are therefore derived from, amongst other things, a knowledge of the
outside surface temperature of the surface under consideration. Since this temper-
ature is mostly not known, it has been suggested (7) that eq (l) be written as
otic
(2)
where the values of Ix-^ and
surface coefficient given by
h.QQ are replaced by a so-called combined outside
h
- T
oc
where Tp is the film temperature,
surface temperature °C,
4e (T Tp
^ T.
(3)
Or the
, Oa the air temperature °C,
Ta the air temperature °K, Ts the surface temperature °K,
the emissivity of the surface and c the Stef an-Boltzman constant.
Roux (7) found that, for South African conditions the combined outside
coefficient was, for practical purposes, constant with a value of 19.873 W/m^ degC
(3.5 Btu/ft^ h degF). Assuming a surface absorptivity for solar radiation of 0.7,
sol-air temperature can be computed from the relationship.
'sa
^oa - I3
(4)
where Iq is the solar radiation in W/m2
In practice in South Africa solar radiation data are summed over hours L.A.T.,
and all other data, with the exception of sunshine, are recorded on the hour, clock
time. Therefore solar radiation data has to be corrected for time, if sol-air
temperature is to be computed.
For computer application the equation of time, employed in determining the
true correction, E, is represented in fourier form as follows :-
E = .005 + .Ol6cos^||^^ - .133sin ^1^^ - .O59cos
4n'n
,169.1n (4™^ _ (fig) .
.OlOsin
where n is the day of year
Programme SELECT computes hourly sol-air temperatures from 08:00 to 16:00
hours for every day from 1 September through 30 April as well as the daily maximum
sol-air temperature. This is followed by a frequency analysis of daily maximum
sol-air temperature. From a cumulative frequency table set up in the computer, the
days on which the daily maximum sol-air temperatures are equal to or higher than the
value that is equalled or exceeded on 10 per cent of the occasions are listed in a
table. This table is then sorted into ascending order of sequence on sol-air
temperature. The sorted table is then printed along with the year and day of the
605
year on which each individual value occurred. The 5 per cent and 2.5 per cent
threshold values of daily maximum sol-air temperature are also determined. The
associated sequences of days are, of course, contained in the 10 per cent tabulation.
Unfortunately solar radiation is only measured at 9 of the 15 stations avail-
able for analysis, so that sol-air temperature cannot be directly computed in all
cases. Hourly solar radiation data can, however, be computed theoretically for
clear sky conditions. If it can be assumed that hot days are free of clouds, sol-
air temperature can then be computed and hot days selected as before. This assumpt-
ion is not generally valid, since clouds appear on most afternoons in summer over
most of the interior. However, at the time of occurrence of maximum sol-air temper-
ature, around noon, analysis of Pretoria and Maion data indicates that it can be
assumed that on the hottest days the skies are relatively cloudless. Consequently
a programme called SOLAR has been written to compute hourly solar radiation totals
(both global and diffuse radiation) for clear sky conditions for stations for which
recorded information is not available. This programme is discussed in more detail
in subsequent paragraphs. At this stage, it will suffice to state that the
radiation data are computed from estimated mean hourly values of Linke turbidity
factor and extra-terrestrial solar radiation fluxes. One of the functions of pro-
gramme SELECT is also to compute hourly values of Linke turbidity factor between
08:00 and 16:00 hrs for the same period of the year as above. This is done for the
nine stations for which solar radiation data are available. From these data some
idea of the mean hourly turbidity climate of the country can be derived, to make a
more reliable estimate of the mean hourly Linke turbidity factor for other places.
The Linke turbidity factor was selected since it is a simple measure of the
haze and water- vapour content of the atmosphere. For total radiation, it gives the
number of clear dry atmospheres that would be necessary to produce the attenuation
of the extra-terrestrial radiation that is produced by the actual atmosphere con-
taining water vapour and haze. In fact, this type of turbidity factor was recom-
mended for meteorological use by the International Radiation Conference of Davos
in cases where only the total solar radiation is measured, i.e., no filter
measurements . (8)
The extinction by haze and water vapour differs from the extinction by pure
air (molecules), and the deviation of the dependence on wave-length of both these
extinctions gives rise to a diurnal variation in the turbidity factor even when the
water vapour and haze content are constant throughout the day. This variation is
generally referred to as a 'virtual variation' and is different for different
water vapour and haze contents. It is for this reason that hourly values of turbid-
ity factor are computed.
The Linke turbidity factor can be computed from the following relationship :-
I = SIq ^ -^T.Sr (m) . m) (6)
where I is the solar radiation intensity at the earth's surface (measured),
Iq = r Iq;^ dX , representing the extra-terrestrial solar radiation intensity,
T the Linke turbidity factor, a (m) the mean value over all wavelengths of the
extinction coefficient in a clean dry atmosphere (Rayleigh atmosphere), weighted
according to the distribution of the transmitted energy (this complex extinction
coefficient depends on the air mass m because of the shifting of the optical
centre of gravity of the radiation as m changes, S = ^2 where R is the radius
vector of the earth and m the absolute optical air mass.
For computer application the value of S can be approximated by a Fourier
series, such as
S = 0.981 + .037COS (f^) (7)
where n is tne day of year.
(If more accuracy is required additional terms can be added.) The relative air
mass is computed from the relationship
606
(8)
where nip is the relative air mass, R the radius of the earth = Km,
p
H the height of a homogeneous atmosphere given by o , where Pq is the atmos-
pheric pressure at sea level = 1.014 x 10-^ Kgm/sec^ ra^ , g the acceleration
due to gravity = 9. m/sec^, "the atmospheric density at sea-level -
1. Kg/m3
Thus H = 8.001 Km
^ = Zenith angle given by cos ^ = sin sin S + cos jzi cos S cost
where ^ is the latitude angle (negative in Southern hemisphere), $ the apparent
IT T
solar declination, and t the hour angle of the sun given by , where T is
time of day.
The apparent declination of the sun can be approximated by a Fourier series,
such as
S =: .009 - .401COS (3^^) + .066 sin (fg^)
- .007COS (^) + .001 sin
- .003COS (^) + .001 sin (^) (9)
where n is the day of year.
Traditionally the hour angle is measured from solar noon. For computer
application it is more convenient to increment time from midnight. Thus the
equation for zenith angle becomes
cos
sin sin S - cos szi cos % cost (10)
PGR a (m), Puessner and du Bols (9) give an empirical relatlon:-
R
e (m) = 0.907m°-°^® (11)
-a
R (m) = - (i*v0.907 + O.Olsinm) (12)
Equation (6) can also be written in the form:
In I = In S + In Iq - THj^ (m) m In e
hence T = P(m) (in Iq + In S - In I) (13)
where P/ \ -
(m)
From the above relations it is now possible to compute turbidity factor.
For future reference and in case some alternative method for computing solar
radiation should be attempted, precipitable water vapour content of the atmosphere
is also computed for the same hours and days as turbidity. The Hann formula (10)
was used for computing precipitable water vapour content from surface vapour press-
ure, viz:
Sj^ (m) m
607
w = c (t) (14)
where w is the precipitable water vapour content in cm, c the proportionality-
constant and e^ (t) the vapour pressure at temperature, t.
Harm gives a value of 0.25 for e. However, the following values were found
for different centres in South Africa.
Table 1. Mean values of the proportionality-
constant C for January and July
Mean value of constant, C
Station
January June
Pretoria (morning)
0
17
Pretoria (afternoon)
0
17
0
13
Durban
0
18
0
12
Windhoek
0
16
0
.13
Bloemf ontein
0
18
0
12
Port Elizabeth
0
14
0
11
Cape Town
0
13
0
12
The surface vapour pressures are computed using the well-known Goff-Gratch
formula .
3 . 2 SOLAR
Programme SOLAR computes hourly global and diffuse solar radiation fluxes on ;
horizontal surface.
Under clear sky conditions for any hour for any place the direct component of
global solar radiation is computed by means of eq (6):
T OT - (T.aR (m) m) , /tc-n
I = SlQe ^ K ^ ^ cos^ (15)
The diffuse component of radiation is computed from a relationship given by
Liu and Jordan (11), viz ;
= 0. - 0.^1) (16)
where T = Idh/loh and f £> = Ich/Ioh ^oh = extra-terrestrial intensi'
of solar radiation incident on a horizontal surface^ = SI cos , I^j^ tne intensity
direct radiation on a horizontal surface, and 1^^^^ the Intensity of direct radiation
Incident on a horizontal surface.
Alternatively
Dh = 60 (. Iqj^ - . I cos |) (17)
where is the hourly diffuse radiation on a horizontal surface.
608
Spencer (12) has found that the coefficients in eq (16) require some adjustment
for Melbourne. However, Liu and Jordan's coefficients will be used until it has
been possible to verify them for South African conditions.
3 . 3 DWDATA
It was stated above that SELECT produces a list of days in ascending order of
daily maximum sol-air temperatures that are equal to or higher than the 90th
percentile of daily maximum sol-air temperature. The punched cards for the various
elements, i.e. hourly drybulb temperatures, hourly relative humidity, hourly wind
speeds and hourly global and diffuse solar radiation values are then selected
according to this list and form the input for DWDATA.
The programme DWDATA is flexible in the sense that, with the aid of a control
parameter, any one of four methods of evaluating design weather data can be select-
ed; and with the aid of a further control parameter, hourly solar radiation data
can either be read from cards or computed.
Briefly, the four different methods of evaluating design weather data are:-
a. Method 1
According to this method summer design data, selected on the basis of daily
maximum dry-bulb temperature, are evaluated. The first step in this analysis is to
determine the mean dry-bulb temperature for each hour of the day, its standard
deviation and maximum and minimum values for all days selected, as described before.
The next step is to select all the occasions when the hourly_temperature of each
hour of the day taken in succession tj_ is such that (tj - 0.5) ^ ^i,j
^ (tj + 0.5) where i refers to the day and j to the hour under consideration and
tj is the appropriate mean hourly temperature for the days selected for each of the
probability levels taken separately. The other weather elements for these occasions
are then selected and their means , standard deviations and maximum and minimum
values computed. A tabulation of the mean dry-bulb temperature and the associated
relative humidity, wind speed and solar radiation values for the various probabil-
ity levels, viz maximum, 2.5, 5 and 10 per cent levels, represents the required hot
weather design data. The programme furthermore computes the hourly solar radiation
fluxes on vertical surfaces facing north, south, east and west, and the following
humidity parameters based on the algorithms published by Kusuda (13): wet-bulb
temperature, dew-point temperature, vapour pressure, humidity mixing-ratio, enthalpy
of moist air, entropy of dry air and specific volume of moist air for each hour for
each probability level. This information is tabulated together with the other
hourly information, referred to above.
The method of computing solar radiation fluxes on vertical surfaces consists
of computing the direct component , diffuse component from an unobstructed sky and
diffuse component reflected from a flat, unobstructed surrounding terrain.
The direct component is simply given by:
Gvi _ Dv,
= ^ „ cos i (18)
V cos 2 ^ '
where, is the direct component of solar radiation normal to given vertical
surface and i the angle of Incidence of direct solar beam on given vertical
surface .
For computing the diffuse sky component, clear and cloudy skies have to be
differentiated. Since no hourly cloudiness data have been recorded on punched
cards it was decided to compute the Linke turbidity factor and compare this with
some threshold value of turbidity factor, the latter being for cloudy conditions,
defined as a sky having approximately one-quarter cloud cover. The turbidity factor
is computed as follows:-
log { S cos^") g
T = \ - Dh J
0.^3^m (In 0.907-0.018 In m)
609
where T is the Linke turbidity factor, Gh the hourly global solar radiation on a
SI
2
9
horizontal surface, w/m , and Dh the hourly diffuse radiation on a horizontal
surface w/m^
Based on an analysis of the data for Pretoria and Maun, a threshold turbidity
of 5.0 seems to be about right.
For computed turbidity < 5.0, the following relationships for computing the
diffuse sky radiation component on a vertical surface have been found for Pretoria
(14):-
for cos i < 0.2:
= Dp^ (0.31 - 0.1 cos i) (20)
for cos i ^ 0.2:
= Dp^e (1-18 cos i - .8) (2i)
For computed turbidity ^ 5.0, the simple relationship (14)
= 0.5 Dj^ (22)
has been found to be valid for Pretoria for average cloudy conditions.
As for the ground reflected solar radiation component, it has been shown (15)
that, for practical purposes, for an unobstructed horizon for Pretoria, this
component can be approximated by
K = ^ (23)
where p = reflectivity of the groimd.
b. Method 2
According to this method summer design data, are evaluated in exactly the same
way as a above, except that they are now being determined on the basis of daily
maximum sol-air temperature in stead of on maximum dry bulb temperature.
c. Method 3
In this case hot day design data, selected on the same basis as in b above,
are evaluated. However, means, standard deviations, maximum and minimum values are
determined for each of the basic and derived elements in the way described for dry-
bulb temperature in a above.
d. Method 4
When the parameter, METHOD, is equal to 4, cold day design data are evaluated.
The basic data are selected on the basis of those daily minimum dry-bulb temper-
atures that are equal to or less than those daily minimum dry-bulb temperatures
occurring on 2.5, 5 and 10 per cent of the occasions for the period under consider-
ation.
The programme DWDATA also arranges the selected information in ascending order
of sequence on year and day of the year. Runs of days when the daily maximum dry-
bulb temperature or daily maximum sol-air temperature, depending on which of these
elements was employed in defining hot days are equalled or exceeded, can then be
readily determined. In a similar way, runs of cold days can be assessed.
In the case of light-weight elements the effects of heat storage capacity is
relatively unimportant. Therefore, there is no significant cumulative effect due to
610
a succession of hot or cold days. However, in the case of heavy-weight elements,
the cumulative effect is very important. This cumulative effect of sequences of
hot days of varying duration can be computed for such elements and related to the
probability of occurrence of sequences of different duration as they actually occur
in practice.
4. Conclusions
In the field of computer application to environmental engineering problems at
the National Building Research Institute in Pretoria, the stress, up to the present
time, has been on producing design weather data for the thermal performance design
of buildings rather than on the development of sophisticated procedures for comp-
uting thermal performance and heating and cooling loads. The philosophy has been
that solutions of such problems can be no better than the physical data on which
they are based, no matter how sophisticated they are. It is believed that the
design data evaluated according to the methods outlined in this paper will, with
perhaps small refinements, provide the basic information required for predicting
thermal performance and evaluating heating and cooling loads with acceptable
accuracy.
5. References
(1) Schulze, B.R. Climate of South
Africa, Part 8, W.B. 28, Pretoria,
Weather Bureau, Department of Trans-
port, (Jan. .)
(2) Van Deventer, E.N. & Van Straaten,
J.F. A rational basis for express-
ing climatic data for use in build-
ing design. In: Proceedings of the
Central African Scientific and Med-
ical Congress, Lusaka, Northern
Rhodesia, 26-30 Aug. , Oxford,
Pergamon Press, (.)
(3) Van Straaten, J.F. & Van Deventer,
E.N. The functional aspects of
building design in warm climates
with particular reference to therm-
al and ventilation considerations.
Int. J. Biochem. Biomet., 8, no. 2,
(Dec. .)
(4) Van Deventer, E.N., Lotz, F.J. &
Boer, P. The assessment of heating
and cooling loads of buildings under
South African climatic conditions.
Fd Inds S. Afr. , XVIII, nos. 10 and
11, (Febr. and March .)
(5) Van Deventer, E.N. Building climat-
ology in Southern Africa. Build
International, 2, no. 7, (Sept.
. )
(6) Mackey, D.O. & Wright, L.T. The
sol-air thermometer - a new instrum-
ent. Heat. Pip. Air Condit. , (May
.)
(7) Roux, A. J. A., Visser, J. & Minnaar,
P.C. Periodic heat flow through
building components - Heat transfer
through homogeneous wall panels
from the outdoor climatic environ-
ment to the indoor air. CSIR Report
no. 71 (formerly DR-9), Pretoria,
CSIR, (.)
(8) Instruction Manual, Part VI, Radiat-
ion instruments and measurements,
London, Pergamon Press, (.)
(9) Fuessner, K. & Dubois, P. Triibungs-
faktor, precipitable water, Staub.
Beitr. Geophys., 27, p. 132, (.)
(10) Hann, J. v. & Silring, R. Lehrbuch
der Meteorologic, V. Aufl. Bd. 1, S.
133. Leipzig, (.)
(11) Liu, B.Y.F. & Jordan, C. The inter-
relationship and characteristic dis-
tribution of direct, diffuse and
total Radiation. Solar Energy, 4,
no. 3, (I960.)
(12) Spencer, J.W. Estimation of solar
radiation in Australarian localities
on clear days. Div. of Building
Research Technical Paper no. 15,
Australia, Commonwealth Scientific
and Industrial Research Organizat-
ion, (.)
(13) Kusuda, T. Algorithms for psychrom-
etric calculations. National Bureau
of Standards Report , Washington,
U.S. Department of Commerce, National
Bureau of Standards, (March 1, .)
(14) Van Deventer, E.N., Dold, T.B. &
Wessels, J. Diffuse solar radiation
on vertical surfaces (to be publish-
ed).
(15) Van Straaten, J.F., Lotz, F.J. &
Van Deventer, E.N. The sun and the
design of buildings for tropical
climates. Presented at the Sympos-
ium on Environmental Physics as
applied to Buildings in the Tropics,
New Delhi, (Feb. .)
611
Quality Rules for Thermal Performance of Low Cost Dwellings
(Building Climatology for Argentine)
R. Alvarez Forn and I. Lotersztain
INTI - Bouwcentrum Argentina
Maipu 171, Buenos Aires, Argentina
Climatic data from the hourly records of the National Meteorological Service were collected from
approximately 22 locations throughout Argentina. These data were then analyzed on the basis of (1)
monthly, seasonal and annual averages, (2) typical hot and cold days, (3) probability of occurrence of
solar radiation, humidity, and wind for typical hot and cold days and (4) probability of N successive
days "equal" to one intitial typical day. Described in this paper are computer programs for the analy-
sis described above and charts and tables developed for the practical use.
Key Words: Climatic data, probability of occurrence of values, probability of runs of N equal
days, typical days.
1. Preliminary
Since the INTI (National Institute of Industrial Technology) and Bouwcentrum Argentina
(Center for Building and Housing Research and Information of INTI ' s System of Centers) are at work
in the complex problem of searching for the minimal higro-thermal requirements to be established for
the housing programs of this country. Up to that year only sporadic efforts of isolated researchers
were recorded in the Argentine Republic. This is then the first research set up with the necessary
means and with the long-range goal of writing down those requirements for the different climatic region
and socio-economic strata of the country. (Ref. No. 1).
2. Steps of the research
The steps or successive goals of this task were laid down as follows:
2.1. To know the climatic zones of the Argentine Republic, for building purposes.
2.2. To define the convenient levels of thermal comfort for different geographical and
socio-economic circumstances.
2.3' To translate those levels into "technical requirements" to be fulfilled by the elements
and/or the whole of the buildings or the urban design.
2.4. To choose experimental controls for the task.
2.5. To put up a theory of thermal comfort and thermal performance of buildings,
useful for the Argentine problems in this area, and based in computer's
capibility.
2.5. To translate the findings into the pertinent legal instruments such as codes, norms,
etc.
oth Civil Engineers
613
5. Chronological developments
This kind of Research is obviously a long-range and long-duration task, with many feed-backs and
probably several re-thinking phases about the whole affair. In this moment we deem it possible to make
fair advances in the three years --. The work's progress is now following the guilding
lines established at the beginning of the period.
Those guide-lines are the steps before mentioned in paragraph 2. In this paper the first step of
the pont 2.1., i.e., deals with the knowledge of the climate of the capital city for building purposes.
This task will be eventually expanded to cover the whole of the country.
4. Source of raw data and processing equipment
Source of raw data is the National Meteorological Service. We have an arrangement made with this
official agency for the access and use of the climatic data recorded in punched IBM cards.
The National Meteorological Service, founded in (by suggestion of the North-American astronomer
Gould) by President D. F. Sarmiento, has now up to 8 million IBM cards with data from many parts of the
country. This data covers the last 15 years.
The cards are the international type used in 700 stations over the world (350 in the U. S.) (Fig. 1)
The type "A" card is prepared for hourly data. In practice it is used with 24 observations/day
and also with 8 to 5 observations/day.
Unfortunately such different type of records are made often at the same place in different periods
or runs of years.
The type "B" card is prepared for daily data or parameters and as such as it records only one or
two values in each 24 hour period.
The type "77" card is used with monthly parameters.
In this research we used only the "A" and "B" types of cards.
For instance, in the first city studied (Buenos Aires) we used a record of 5 years with hourly data
and another, also of 5 years, with data at the hours 2 and 8 a.m., and 2 and 8 p.m. These data come from
the station "Central observatory" placed near the geographical center of the city. We have only two othe
stations in the city and it outskirts with data in punched-cards . One is by the River Plate and the
other about 25 km inland. We hope to check those stations' data with the former, in a later phase of
our task.
The IBM machine works with disks (each capable of 248.000 words).
This computer is in the CITMADE (INTI's computer center) and our research has a part-time arrange-
ment for its use.
Climatic parameters for building purposes in typical hot or cold days
1. Goals of the Work
This research aims at the statistic specification of all the relevatn climatic parameters of a
"typical hot day" and a "typical cold day".
Those days are to be selected following statistical criteria with 2 different levels of complexity.
We deem this work suitable for calculations and specifications in the following fields.
(a) -Design of buildings and/or its parts for suitable thermal insulation, good natural venti-
lation, efficient vapour barriers, convenient sun exposures, etc.
(b) -Urban design of new communities and housing schemes, etc.
(c) -Design of heating, ventilating and air conditioning installations or appliances, from
the following points of view:
i. Outdoor design basis for the project,
il. Outdoor conditions for testing purposes.
614
2. Summary of the first task
The first task was then to get acquainted with the climatic parameters of different zones and/or
cities of this country.
As the climatic parameters as [jrocessed by the standard methods of our National Meteorlogical
Services for other ends were inadequate for building purposes, it was decided, then, to process the raw
data (in the form of IBM cards provided by the NMS) in the CITMADE's computer, following several new
programs written down especially for this goal. The plan is to record the data in up to a million cards
of the NMS in about 12 disks, according to those programs. These data are from about 20 cities or re-
gions of the country. It is expected to develop such work in a span of about 3 years.
The hypothesis laid down for the task were these:
(h-i) The design conditions must take into account all the pertinent climatic parameters:
(a) air temperature
(b) humidity (by one or more of the several variable used for measuring it)
(c) speed and direction of the mind
(d) sun radiation
(h-ii) The study of the parameters one by one was deemed not satisfactory in this problem,
so we stated that the statistical probability of concurrence of typical values of
those variables had to be worked out.
(h-iii) A "typical hot day" and a "typical cold day" had in turn to be analyzed hour by
hour and the results submitted to a statistical probability analysis in order to
fulfill the item (h-ii).
(h-iiii) The probability of occurrence of successive runs of 2, 3, N typical hot-days and
typical cold-days had to be worked out.
3. Main features of the Argentine climate
This country stretches from 22° to 55° south latitude, and besides has several territories further
to the South, on islands and a segment of the polar continent. On the mainland we have the following
broad climatic zones: (each zone is subdivided in two, as shown in the map , fig. 2).
i. Hot: 1 - humid; 2 - dry
ii. Temperate: 1 - humid; 2 - dry
iii. Dry: 1 - semi-arid; 2 - "patagonic"
iiii. Cold: 1 - dry; 2 - "humid"
Nevertheless, the geographic and seasonal climatic variations are not so marked as in the N. W. or
central U. S. or central and east Europe. This is because South America is really a tongue of land
between two huge masses of water, the South Atlantic and the South Pacific Oceans; and the Polar Cape
is more than 1.000 km. South of Cape Horn, the tip of the Continental Block and adjacent islands. But
the long Cordillera de los Andes forming the West limit of the country (about 2.500 km) is really a
great "climatic dam" and a decisive factor of our climatic patterns; it produces marked alterations in
the overall atmospheric circulation, and superimposes an West-East influence over the normal North-
South axis of climatic levels.
The most remarkable climatic factors are: hot summers in NE , NW and W zones; mild conditions in
both seasons in the Center; cool and very windy in the lower half (Patagonia). Snow is a problem only
in high motintain and plateaux zones. The East half of the country has abundant rains, but the rest is
under the level of 500 mm (20 inches) in the average year and so, under the minimum rain level for
agricultural purposes (except zone in the N.W. and other in the southern cordillera and the island of
Tierra del Fuego, both cold and rainy).
2 2
The first region occupies about 1.700.000 km and the second 1.000.000 km . More than 3/^ of the
total population of 22 million inhabitants live in the humid region.
615
4. Fundamental criteria for choosing and describing the typical or
design day (hot or cold)
One climatic parameter was to be chosen as the fundamental, and the probability of concurrence of
values of the other three (excepting precipitation) to be studied.
The first one had to be the most important for the higro-thermal state. A review of the climatic
zones of our country showed that not always the temperature of the air - the best known and more often
used parameter - seems to be the best choice. Maybe the solar radiation in the hot zones or the wind
in the Patagonia would be better. But for the sake of uniformity and also because the temperature of
air has always the best record in each locality, this was our choice for the role of "leading parameter".
As mentioned before, the work was begun with Buenos Aires and we used type "A" (hourly) and type "B"
(daily) IBM cards. For the 5 years to we had hourly data and for the next 5 years to
we had only data from 2 and 8 a.m. and 2 and 8 p.m. In both runs we had also the daily card of the
"B" type. (Fig. 2 shows the two cards and the relevant items of the punching-code used by the NMS) .
The first computing task was to get the usual average, maximum and minimum values of the relevant
variables. This was checked with other period's results, giving in general a good agreement (of course,
up to this point the work was rather of the usual climatic type). (Fig. 3) ■
The second task was different and implied an entirely new approach - at least for our country -
aimed at the determination of the design days, for building purposes.
This was done as follows:
4-1 The ogive of the average daily temperatures of the 3^50 days (10 years, without the 29th
of February for the sake of simplicity) was worked out in absolute and relative frequencies
by the computer. Let's call "p" the cumulated relative frequencies.
4-2 For each of the levels of p = 2,5%, 5%, 10%, 90%, 95%, 97 ,,5%, and 99%, we worked out the
steps that follow.
Here we give the general explanation for the p = 2,5% level, because we take p = 2,5%
for the typical cold day, but in the graphs and comments we give also the results for
the p = 97,5% level for the typcial hot day.
4-3 The machine was ordered:
(a) to find the p = 2,5% day and pick up its card;
(b) to pick up the cards of the "next" ten days over that day;
and the "next" ten days below that day. "next" means here the
days whose cards showed average daily temperature numerically
(not chronologically) in the neighborhood of the p = 2,5% day.
4-4 For this set of similar 21 days the machine then did the following:
(a) worked out the relative frequencies of average values of temperature,
humidity and insulation (Fig. 5)
(b) worked out the average hourly temperature, i.e., the average 1 h,
2 h, 3 h, 24 h temperature; with those values we traced
the curve (Fig. 4)
(c) the same calculations were made for the relative humidity, hour by
hour and also the curve was traced (Fig. 4)
(d) worked out the frequency of the wind in 8 directions and one
"no-wind" state, also hour by hour. The machine also got the average
speed for each direction. (Fig. 5 bottom)
(e) in the drawing (Fig. 5, lower) for the solar radiation we used
"heliophany" or relative insulation parameter (the ratio of the
real sunny time of a day to the astronomical one) and with such
basis we made the calculation of the average direct sun radiation
on 8 vertical planes and the horizontal plane. (Fig. 6).
For the typical hot days see Figs. 7, 8 and 9.
The radiation values were worked out using the tabulated
616
results of a sun thermal radiation program prepared
by Architect Victor Olgyay, and generously given to
us during his stay in Bouwcentrum. (Ref. 14)
The program was processed in the IBM machine and gave
for each degree of latitude and for the mid-month day
the before-mentioned radiation values, for a theoreti-
cally cloud free and clean air day. Those values are
then the maximum possible ones. For Buenos Aires we
used the latitude 34° 1/2 South.
In order to get the real magnitudes, these theoretical
values were affected by a "F" factor, less than the
unit established for Montevideo (a city only 200 km
from Buenos Aires and almost in the same latitude) in a
statistical calculation summarized in appendix "A".
As the two cities have very similar climates, we felt
that we could use values of the insulation factor "F"
of Montevideo for our work about Buenos Aires (Ref. No. 2).
4- 5 Another useful statistical criterium was used: the machine worked out the proba-
bilities of chronological runs of 2, 5 N successive typical cold
days, following this sequence (Figs. 10 and 11):
(1) we had established before the average temperature of
the "first" cold day and chosen the respective card
(paragraph 3, item (a).
(ii) the machine then worked out the probability of having the
next day with an average temperature equal or less than the
value of this parameter in the "first" cold day (item (i);
and also the probability of having 3; ^ 10 successive
"cold days" so defined. Of course, in the case of the
typical hot day, in the item (ii) we read "equal or more"
instead of "equal or less".
(iii) then it did the same with an allowance of + 1°C and
+ 2°C for the typical cold day's average; and I'C and
2°C for the typical hot day's average.
5. Comments and remarks
Several comments and remarks could be made on the method just explained. We state here
a few of them:
5- 1 of course, the "desing days" obtained with such processes are a kind of
statistically representative or meaningful days, for the hot or cold condition
studied.
The various parameters will evolve, during such a day, in a typical manner,
represented by our tables and graphs.
5-2 In the typical cold day it is observed that:
(a) the lowest temperature is above the freezing point
(+ a.y'c)
(b) the wind blows from the W or SW at the coldest hours
(c) the sun shines bright, it is a clear day
617
(d) the daily span of the temperature is significant
(9.3°C)
(e) the humidity has also a marked oscillation being
very high at the coldest hours, and rather low at
the hottest hours
(f) the probability of chronological runs of such days
goes down very fast and is negligible after a few
days
5-3 In the typical hot day it is observed that;
(a) the maximum temperature is moderately high (+ JS'C)
(b) the wind blows from the N, NE and E in the hottest
hours
(c) the sun shines brightly - it is a clear day
(d) the daily span of temperature is significant (9°C)
(e) the relative humidity has a marked oscillation, being
low at the hottest hours (457i,)
(f) the probability of chronological runs of such days goes
down very fast and is negligible after a few days
5-4 The findings are of interest from several points of view:
(a) from the standpoint of the thermal lag of buildings
(b) from the standpoint of the heating or conditioning system,
their thermal lag and the control systems to be used
(c) from the standpoint of the possible use of analogue computers
for simulating the conditions (electronic or hydraulic)
(d) from the standpoint of the possible use of digital computers
for the same end (i.e., for resolving the electrical circuit)
(e) from the standpoint of the different levels of probability
likely to be used in different problems
On the points (a) and (b) it can be said that in this city
it is important to have a heating or winter conditioning
system with great "time flexibility" and with zonification
according to the rose, i.e., "spatial flexibility".
This is because of the important daily oscillations of temper-
ature and the high solar radiation at the NE; N and NW expos-
ures .
The summer service of air conditioning in buildings with
great exposure requires also, both flexibilities, as the
typical hot day shows.
The prevailing winds blowing from the N, NE and E in those
hot days can be used for natural ventilation of dwellings,
schools, industrial buildings, etc., not equipped with air
conditioning.
618
It is also possible to see that light buildings can be
brought in "resonance" with the exterior conditions
(transient period 1 to 3 days, for instance), but heavy
structures cannot attain such condition (transient periods
from 4 days up). This problem is very important for low-
cost dwellings in summer, because it is not economically
possible to furnish such houses with air-conditioning
appliances and therefore, it is necessary to study the
spontaneous evolution of the internal conditions as a
function of the external ones, (a very difficult problem
from a physico-mathematical point of view) .
About the points (c) and (d) , it is obviously necessary
to know the chronological recurrences of such days in
order to simulate the real situation in the computers.
(f) This study shows only the results for the "2,5% day" as
a typical cold day and the "97,5% day" as the typical
hot day. Hovjever, we worked out, as stated before, the
levels Ps 17o, 5%, lOX, 907„, 95%, and 99% because we felt
that for idfferent problems it may be necessary to use
such different levels.
Of course, with the levels 5%, 10%, 90%, and 95% the
"character" of the typical cold or hot day is not so
well marked and it is a matter open to discussion as to
the meaning of such days.
We want to state here our thanks to the authorities of
the following instiuttions for their decisive support
to this research:
INTI (National Institute of Industrial Technology) ;
CIBA (Bouwcentrum Argentina, Center for the Research
and Documentation in the Building Industry);
CITMADE (Center of Mathematical and Computer's Techniques);
SMN (National Meteorological Service).
Appendix "A:
Factor (f) of conversion of the sun thermal directo radiation for clear sky in the value
for mean sky (R2) taking into account the insulation and the nubosity (Ref. No. 2).
These auxiliary symbols are used: Rl direct radiation for clear sky.
Insolation; (%) I = Real time with bright sun/Astronomical length of the day
NOTE: Insolation is called "heliophany" in the figures.
N = Geometrical area of the sky
Clarity: (%) C = 100 - N
The paper (Ref. No. 2) shows that with an error not in
excess of 4% for Montevideo it is correct to write:
619
F (%)
This factor is to be applied to any hour in the day if
that day has insolation I (?„) and nubosity N (7o) = 100 - C (%) ,
and gives for those conditions.
The day in question can be a single one or a statistical
average day.
Further, the paper shows that the coefficient M = I/C has in
Montevideo a maximum value of 1.461 and a minimum of 1.327.
This means that it exists in fact a correlation between the
values of I and C as can be expected, and this justifies the
use of F.
Appendix "B"
Prehistory of this paper
The choice of the statistical criteria for this study was the result of a rathe?' long
process. Maybe it is interesting to outline its principal steps. It must be remembered
that we started with a totally new approach in our country, and we had only foreign biblio-
graphy on the subject; then we made the following remarks in the course of the studies:
First: We were at a loss when we tried to understand clearly the reasons that several
researchers had in mind when they stipulated their climatic parameters for
building purposes. Such reasons were not explained, or maybe were not good
between-lines readers (Refs. 3, 4, 5, 6 and 7).
Second: We felt that in order to adapt, modify or reject some of this pre-existent
work, it was necessary to gain knowledge about such a background.
Third: We deemed necessary to find a way to state not only the parameters as if its
influences over the building and the human comfort were independent of the
others, but also in their mixed or complex effects. As an example, the
Sol-Air theory (Ref. 8) showed a good advance towards such an "upper level"
of complexity, fusing the sun radiation and the heat of the air in one
parameter.
Fourth: We saw that, for obvious reasons, in each country the parameters and criteria
related to the outstanding characteristics of their climate were those more
studied. This showed that for our purposes it would be necessary to study
with special dedication the technical documentation produced by countries with
climates not very dissimilar from ours. And between these, the papers about
the problems in temperate, hot-arid and hot-humid regions were the most use-
ful because the thermal comfort is more difficult to attain in those circum-
stances than in the moderate cold prevailing in our winters (Ref. 9, 10,
and 11).
All this boiled down to the following "obvious" remark; The building
climatology is a science "in the making" and as such shows plenty of dis-
agreement between authorities, not only about the answers, but also - and
maybe in the first place - about which are the problems.
An illunimating paper came then in our hands (Ref. 12). Here the two authors
stated clearly what we had been searching for: the basis for new criteria in
the "upper level" in question.
620
It is an act of justice to mention here that one of us was in England during
6 months of , working with Professor A. Pratt (Ref. I3) , and that during
three months of , we had the technical assistance of Professor Victor
Olgyay (Ref. 14). Working and discussing with those authorities was a very
useful experience for our background.
We decided then, to try our hand at the problem, reduced for the first effort,
to the definition of the typical hot and typical cold days working in such
an "upper level" of complexity, and using Buenos Aires climatic data.
For this we made, as a first step, a classification of all the parameters
used for the others researchers following several criteria:
i. extensive, specific and intensive variables
ii. types of periodic functions approached by these
iii. possible useful combinations of variables in
the "upper level" of complexity
iiii. miscellaneous.
And finally, with all this background, we asked ourselves: what is a hot day in Buenos
Aires like? - A cold day? How would such a day affect the thermal comfort of a person? And
the thermal performance of buildings? - And with those "simple" questions in mind we write
down the criteria to be used by the programmer of the IBM machine and we passed the question
and the answers over and over again through this filter. Up to now, the results are des-
cribed in the present paper. . . . and this is the little story about the making of such research.
References
(1) R. Quintela C. Vasino, "Bases de. la clima^
tizacion artificial en Buenos Aires", Meteo
ros (octubre-diciembre ) .
(2) R. Rivero,. "Calculo de la energia termica de
la radiacion solar directa y difusa en va-
ries pianos. Para Montevideo", Montevideo
(Uruguay), Facultad de Arquitectura , Monte-
video, octubre .
(3) A. Fournol, "Climats et habitation, cahiers
du centre Scientifique et Technique du Bati
ment", Paris, France, Livraison 25, Cahier
223.
(4) J. Borel, "Notice technique pour 1' applica-
tion du reglement de la construction en Al-
gerie" idem, Livraison 57, cahier 456.
(5) Reef 58 Vol. II, Paris, . Recueil. Sec-
tion D5, Hygrothermique et ventilation.
(6) H. Reiher y D. van Zuilen, "Report on the
symposium regarding the problem of the ef-
fect of climate upon building", GIB Bulletin
No. 3 ().
(7) American Institute of Architects. House
Beautiful, Climate Control Project, Re-
gional Climate Analyses and Design Data,
for 15 cities and regions of the USA
(AIA Journal - passim).
(8) Sol-air theory applied to the orientation
of Buildings, (pgs. 54-62 of book Ref. 10
below)
(9) A. van Straaten, E. van Deventer, "Thermal
Performance of Buildings", Amsterdam, .
Elsevier Publishing Company.
(10) V. Olgyay, "Design with Climate", Princeton
(USA), . Princeton University Press.
(11) Directives communes pour I'agrement des Pro-
cedes de Construction par Grands Panneaux
Lourds Pref abriques , (UEATG) , Cahiers du Gen
tre Scientifique et Technique du Batiment,
Paris, France. Livraison 80, cahier 696.
(12) E.N. van Deventer and J. F. van Straaten, "A
rational basis for assessing Climatic Data
for use in Building design", National Build-
ing Research Institute. Pretoria (South Afri
ca), .
(13) Prof. A. W. Pratt, Head of Department of
Building, Aston University in Birmingham;
directs research in thermal problems of
building.
(14) Prof. Victor Olgyay (-). Worked
with his brother Aladar Olygyay (-
) at the Princeton School of Archi-
tecture, in the field of architecture and
climate.
621
622
623
TEMPIP»TURA t-.tn'Mlk
MEDIA Y M'NIM*
MFNSUAl IC I
BUENOS AIRES
GRADOS OIAS
(base y ba»e ]8rCD>
_[=JL
PRECIPITACION MAXIMA.
MEDIA V MINIMA
MENSUAL ImmJ
//VT-/ - c/ ooc/yvcavmM'f
Figure 3. Standard climatic data of Buenos Aires
624
625
DIA T/nCO A/W
NivcL tsy.
TCMTCKATUKA
«.# :» «.7 c* <.v
-T-
m
'■''///,
m
m
m
r.'
' ' ' "/
o
a
no
IS
ao
as
30
3S
40
*e
ao
m
as
ao
m.
■IB
ao
m
i
f cm • 2 6 m /s<5
Figure 5. Average values of temperature, humidity and wind frequency for typical cold days
626
627
628
629
DIA TinCO CAUDO
9 x> rs so
OB ^ -XXK 'HCCKPG OC
Figure 9. Average values of temperature, humidity and wind frequency for typical hot days
630
631
d
t
632
Fortran IV Program to Calculate z-Transfer
Functions for the Calculation of Transient
Heat Transfer through Walls and Roofs
G. P. Mitalas and J. G. Arseneault
Division of Building Research
National Research Council of Canada
Ottawa
The heat transmission matrix for a wall or roof has elements
A, B, C and D; i.e.,
e
o
A
B
e.
1
Q
o
C
D
Q.
1
where 9 = Laplace transform of surface temperature, and
Q = Laplace transform of surface flux
The elements A, B, C and D are functions of the thermal properties,
thickness and position of materials in the wall. When the boundary-
conditions are of the first kind (i.e. when 9 and 9. are given), the
fluxes are given by
Q
o
1
D ,
-1
9
o
Q.
1
B
1 ,
-A
9.
1
and when boundary conditions are of the second kind, the equations
invert to
9
1
C
A ,
-1
Q
o
9.
1 ,
-D
o
Q .
X
1
The program presented in this paper evaluates the coeffi-
cients of a set of z-transfer functions that are equivalent to the
Laplace transfer functions D/B, 1/B, A/B, A/C, l/C and D/C.
These z-transfer functions relate to the z-transforms of the surface
temperatures and heat fluxes in the same way as their counterpart
Laplace transfer functions relate to the expressions above.
Research Officer and Computer Systems Programmer, respectively.
633
The program will evaluate z-transfer functions that are
exact for either a unit step input, a ramp type input or a periodic
input with specified harmonic components. The user can choose,
therefore, the option that best suits a particular problem.
Key Words: Frequency response, roofs, transient heat
conduction, walls, z-transforms.
The heat transmission matrix for a wall or roof has elements A,B,C and D, i.e. ,
e
o
A
B
e
1
Q
o
C
D
Q.
1
where 9 = Laplace transform of surface temperature
Q = Laplace transform of surface flux
The elements A, B, C and D are functions of the Laplace parameter, s, and of the thermal properties
thickness and position of materials in the wall. When the boundary conditions are of the first kind
(i.e. when 9 and 9. are given), the fluxes are given by
Q
1
D ,
-1
9
o
o
Q.
B
1 ,
-A
9.
1
1
and when boundary conditions are of the second kind, the equations invert to
e
o
1
A ,
-1
Q
o
9.
1
~ C
1 ,
-D
Q.
1
The program presented in this paper evaluates the coefficients of a set of z-transfer functions
that are equivalent to the Laplace transfer functions D/B, 1/B, A/B, A/C, l/C and D/C. These
z-transfer functions relate to the z-transforms of the surface temperatures and heat fluxes in the
same way as their counterpart Laplace transfer functions relate to the expressions above.
The program will evaluate z-transfer functions that are exact for either a unit step input, a
ramp type input or a periodic input with specified harmonic components. The user can choose,
therefore, the option that best suits a particular problem.
2
1. Calculations of z-Transfer Functions [Ref. 1]
The z-transfer functions for a multilayer wall can be calculated in two ways:
Method 1 consists of choosing either a step or a ramp input function, I(z),
and evaluating the output, 0(z), that corresponds to l/ s or 1/ s^ times one
of the Laplace transfer functions. The related z-transfer function is de-
termined from 0(z)/l(z).
The literature reference is at the end of the main text of this paper.
634
Method 2 involves solving a set of simultaneous linear algebraic equations
to obtain the coefficients of a z-transfer function whose frequency response
matches the exact frequency response of the multilayer slab at certain selec-
ted frequencies.
The z-transfer function corresponding to any one of the Laplace transfer functions can be ex-
pressed as the ratio of two finite polynomials, N(z)/D(z). The denominator, D(z), is the ssime for all
the transfer functions that have a common denominator in their Laplace transfer function equivalents,
and is the same for Method 1 and Method 2. The procedure for finding the coefficients of the denom-
inator polynomial involves two steps.
(1) Determination of the poles of the associated Laplace transfer function: .
i.e., find 3 , the roots of B = 0;
n
or Y > the roots of C = 0;
n
The elements of the transmission matrix for a wall have an infinite set of roots, which lie
along the negative real axis in the s -plane. The position of the roots depends on the di-
mensions and thermal properties of all the layers, and cannot be expressed in any simple
way. The necessary poles can be found numerically, however, by evaluating the functions
B or C for a sequence of negative real values of s. This program evaluates the roots of B
between zero and -30/A , and the roots of C between zero and -450/A , where A is the
specified sampling interval of the z-transform.
(2) The evaluation of the product:
-& A
D(z) = n (1 - e " z' )
when the parent Laplace transfer function has the element B in the denominator, or
-Y A
D(z) = n (1 - e " z' )
when Laplace transfer function has C in the denominator.
Methods 1 and 2 differ only in the way the numerator polynomial is determined. Method 1
requires the evaluation of the time function that corresponds to l/ s (step input) or to l/ s^ (ramp input)
times the appropriate Laplace transfer function, for t = A, 2A, 3A, The coefficients of 0(z)
are evaluated by finding the residues of the Laplace transfer function at the previously determined
poles.
The numerator (N(z) is then evaluated using the expression
N(z) =
D(z) . 0(z)
I(z)
where I(z) = — for a step input
1 - z
I(z) = j— ^ for a ramp input.
z(l - z )'
635
Method 2 requires the evaluation of the Laplace transfer function of the wall at s = io) , and the
calculation of the denominator D(z) at z = where lUj^ is the angular velocity at which the
z-transfer function is to match the exact frequency response. This gives a pair of equations for each
value of uUj^ (i.e. real and imaginary parts are equated separately) except at - 0-0 (i.e. steady
state) where only the real part of the equation exists. The resulting set of equations for a series of
values of can be expressed in matrix form, viz. :
1
1
1
1
1
1
L
^0
A(0)
1
Cosuu^A
Cos2uUj A
CosJuu^A
^1
X(a^)
0
SinuUjA
Sin2(U^A
SinJuo^A
^2
Y(a)j)
1
CosUJ^A
2
Cos2uu,A
2
CosJou^A
2
^ 2'
0
SinOJ^A
Sin Ziu^^
SinJuu^A
where the a's are the unknown coefficients of the N(z) polynomial and X(a)^) and Y((JUj^) are real and
imaginary parts of the product of the Laplace transfer function and denominator D(z) evaluated at
ia)„ A
s = iuUj^ and z = e respectively. The solution of this matrix equation gives the unknown coeffi-
2n
cients. It should be noted that in setting up this matrix, uu^ > should not be used since higher
frequencies than this tend to give poorer results.
2. General Description of the Program
This Fortran IV program is designed for an IBM -360 computer with line printer. Appendix A
consists of the coding sheets (A-1 to A-20), a sample of output (A-21 to A-25), and the flow diagrams
(A-26 to A-31) for this program.
The program can handle slabs that are comprised of no more than 20 layers of homogeneous
material and no more than 100 significant poles. The poles are evaluated to 10"-'^'^ precision, and
the limit for the numerator and denominator series of the z-transform is set at 10"'^. At least one of
the layers of the composite slab must have significant heat-storage capacity.
The program is designed to operate continuously; i.e. , after the z-transforms for one wall
have been completed, the program automatically reads the data for the following calculation. The
program terminates when A = 0. 0 is read.
2. 1 Input
Card 1 Sampling time interval A
Format: (F 10.3)
Card 2 and 3 Description of the slab for title purpose only.
Format: (80 Al)
Cards 4 to I Groups of cards giving thermal properties, thickness, and description of the
layers. Whenever applicable, the first card of the group contains values of
thickness of layer,
thermal conductivity,
density,
636
specific heat, and
resistance of radiation path.
Otherwise, the first card contains the thermal resistance of a layer that has
negligible heat storage capacity.
Format: (5F 10.4)
The second, third ... or more cards of the group can be used for the descrip-
tion of the layer if an integer is inserted in Column One.
Format: (30 Al)
Card I + 1 Blank card to terminate the above input of thermal properties and their de-
scriptions.
Card 1+2 Code number, ICASE, and the number of frequencies, NW, to be fitted when
Method 2 is to be used (see Table 1).
Format: (II, II)
Card 1+3 This card is read only when ICASE = 2 or 5. It specifies the periods of the
harmonics to be used in frequency response calculations.
Table 1. Code Number ICASE
Input
Function
Boundary
Condition
Method 1
Method 2
Square
Pulse
Triangle
Pulse
Group of
Harmonics
First
Kind
Invalid
Combi-
nation
1
2
Second
Kind
3
4
5
3. Reference
[1] Stephenson, D.G. and Mitalas, G.P., Calculation of heat conduction transfer functions for
multilayer slabs. Submitted to ASHRAE for presentation January .
4. Acknowledgement
The authors gratefully acknowledge the many helpful suggestions made by Dr. D.G. Stephenson.
This paper is a contribution of the Division of Building Research, National Research Council of
Canada, and is published with the approval of the Director of the Division.
637
START
\ INPUT
— \ FROM
\ CARDS,
INPUT
FROM / DT
CARDS
EVALUATE
INVERSE
LAPLACE
TRANSFORMS
AT t = A,2A...
CALCULATE
THE
COEFFICIENTS
OF N (Z)
->-
CALCULATE
THE COEFFICIENTS
OF D (Z)
= 2 OR 5
ICASE > >
METHOD I
CALCULATE
RESIDUES AT
THE POLES
CALCULATE
RESIDUES AT
THE ORIGIN
1,3 OR 4
/subroutinen
\ origin
-<-
METHOD 2
SET UP THE
SQUARE
MATRIX
'SUBROUTINE^
, FREQRE /
CALCULATE RHS
OF MATRIX
EQUATION
i.e X(W),Y(W)
OUTPUT
ON
^PRINTER/
SOLVE MATRIX
EQUATION FOR
COEFF OF
N (Z)
* DETAILED ON FOLLOWING PAGES
MAIN -PROGRAM
Figure A-1. Flow diagram for z-transfer function calculation program.
638
LAST= 0
I ROOT = 1
SET Rl
AND R3
YES
store : roots
functions
and derivatives
in its proper
ORDER
REPLACE EITHER
Rl OR R2 BY
RTEMP SUCH
THAT Rl AND R2
ARE OPPOSITE
IN SIGN
SUBROUTINE
MATRIX
Rl> Fl -FPI
LAST = LAST + I
^ I
.LAST
( RETURN )
Rl =ROOT (LAST-i;
R3 = R00T (LAST)
I = I
R2 = Rl +
(R3-RI)
20.0
* I
SUBROUTINE \
-^—{ MATRIX j >-
R2-* F2-FP2/
I -21
CHECK FOR
TWO CHANGES
IN SIGN
FPI ■* FP2
CHECK FOR
CHANGE IN
SIGN FROM
F I ^ F2
^0
NO
1 = 1 + 1
«* NOTE
Rl = O.OOOI/DT
R3 = R00T (LAST)
IR00T=IR00T+l
CHECK FOR
CHANGE IN
SIGN FROM
F 1 * F2
> — <
/SUBROUTINE
MATRIX
R2^F2
I ROOT =
I ROOT-I
LAST =
LAST-I
R2 = Rl +
J * (R3-RI)
I = I
NN= 10 * I
J = I
J-NN
<0
>0
' >
1 = 1 + 1
> <
DETAILED ON FOLLOWING PAGES
ABNORMAL
TERMINATION
WITH MESSAGE
** NOTE
DUE TO ORIGINAL SETTING OF Rl AND R3 THIS PATH
WILL NEVER BE TAKEN THE FIRST TIME THROUGH,
i.e. WHEN CHECKING FOR THE FIRST ROOT.
SUBROUTINE - POLES
Figure A-2. Flow diagram for determination of poles of Laplace transfer function and calculation
of the values of A, B, C, D, and their derivatives at these poles.
639
START ^ — >
F =0.0
F = F + F3(J-i)
* F3(J)
F3 (J) = F
FF=FF+F
J = J+ I
F3(J)= F2(J)
1 = 1+1
FF
= 0.0
—
YES/ ARE
-< — 0
I-M >— e
1=1+1
Fl(i)=F
F=F + FI (l-i)
* Fl (1)
SUBROUTINE - MATRIX
Figure A-3. Flow diagram for the evaluation of A, B, C, D, and their derivatives for any real
negative value of s.
640
START y-
MP = 0.0
MPP = 0.0
ELEMENTS OF
- TRANSMISSION -
MATRIX A(II
DERIVATIVE Of
- TRANSMISSION -
MATRIX B(II
SECOND
DERIVATIVE OF
" TRANSMISSION "
MATRIX Cm
I-l
1=0
<— E=e(ii
TEMP =
D»F
TEMPI =
E«G
MPP=MPP
+TEMPI
K= I
1-M
>0
MP=Bli)
MPP=C(il
RETURN^
SUBRROUTINE - ORIGIN
Figure A-4.
Flow diagram for the evaluation of first and second derivative of A, B, C and D at
s = o.
641
CALCULATE
TRANSMISSION
MATRIX ELEMENTS
FOR W(j) AND
LAYER I
( RETURN )
>0
J-LW
^0
J = J + I
A(J) = MMM
MMM=MM
M M M M ~
MMMM +
MM^MMM
MMM=MMMM
>0
1=1+1
SUBROUTINE - FREQUE
Figure A-5. Flow diagraxn for the evaluation of A, B, C and D for pure imaginary arguments.
642
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668
Application of Multilayer Periodic Heat Flow Theory
To the Design and Optimization of Roofing Systems
C. P. Smolenski and E. K. Halteman
Pittsburgh Corning Corporation
Pittsburgh, Pennsylvania
and
E. M. Krokosky
Ca rneg i e
Pi ttsburgh
Mel Ion I nst i tute
Pennsylvania
Techniques for studying the periodic heat fluxes through multilayered roof
systems subject to equivalent sol air input driving functions have been coupled with
a multi-functional optimization procedure for the selection of material components,
which, when combined into a roof section, will satisfy certain object functions.
The object functions can be any or all of the following type: maximum thermal lag,
minimum total integrated flux, minimum peak flux, minimum temperature variation of
the most temperature susceptible material, minimum cost, minimum weight, and others
related to purely structural consideration such as deflection, stresses, etc.
A computer program has been designed such that a search is made through a
directory of roofing materials in order to select the right combination of materials,
both from a dimensional and property standpoint as well as actual position within the
roofing section. The basis of the optimization procedure is a generalized multi-
variable optimization criteria that essentially compromises the design objectives
and is capable of handling any number of additional inequality constraints.
The multi-layer boundary value problem for temperature and flux at any position
within the layers was solved by use of the Lapace transform which converts the partial
differential equation of linear heat flow into an ordinary differential equation which
is then solved in matrix form. When incorporated into the optimal design procedure
the multi-layer heat flow theory gives the designer or analyst a powerful tool for
studying roofing design.
Specific design examples are presented to show the importance of material
selection and sequence of material layers on the most critical components of the
roofing system. The multitude of choices possible in terms of combinations of
materials, thicknesses and sequence of layers precludes solution other than by
computer.
Key Words: Built-up roofing, optimization, periodic heat flow theory,
roof design, sol-air temperature.
Research Engineer and Research Physicist, respectively.
Associate Professor.
669
./ , 1.1 ntroduct ion
Over the last twenty years, there has developed an awareness of, and a concern for premature fail-
ures of built-up roofing systems. Various sources have estimated that annually ten to fifteen percent
of the installed new roof systems will ultimately fail prematurely; i.e., within one to five years
after initial installation [1].^
There are a large number of different types of failures and associated factors causing the
failures[l]. Many failures can be directly attributed to poor design, poor workmanship, poor installa-
tion, or simply attributed to the hostile environment in which the built-up roofing must function.
Cullen [2] [3], Handegord [^] and Joy [5] have singled out thermal cycling and solar radiation exposure
as two of the most important factors influencing roofing membrane durability and integrity. Specif icall/
thermal cycling can be related to thermal shock and thermal expansion-contraction movements, while the
solar radiation can be related to photo-oxidation of the asphaltic materials.
Some knowledgeable researchers [I] in the field of roofing design have suggested that roofs should
be designed so as to provide a more favorable environment for the waterproof membrane. To quote Baker,
"Either improve membranes to withstand the harsh real world environment, or protect the membranes from
the environment." The economics of conventional built-up roofing being what they are, it is unlikely
that they will be replaced in the near future. Therefore, the protected membrane system is the more
likely to offer immediate solutions to the problem.
In order to protect the membranes, it is necessary to determine the thermal fluctuations of the
felts. In order to do this, it is necessary to have an analytical technique for handling multilayer
periodic heat transfer. However, the choice, location and thickness of the insulating material to
protect the felts is governed by certain performance characteristics for the roofing system as a whole.
The former aspect of this problem requires a thermal model for multilayer heat transfer while the later
aspect of the model requires a multi-object function optimization scheme. The purpose of this paper is
to present a combination of an analytical model for heat transfer and an optimization scheme which will
be used to design a roofing system to protect the roofing felts from thermal fluctuations but at the
same time provide a suitable thermal barrier at a reasonable cost.
2. Roof Model
For purposes of illustration and comparison, a relatively simple roofing model was chosen, see
figure 1. The three major components of the roof system are the structural deck, in this case a concrete
slab, the insulation, arbitrary, and the built-up membranes, i.e., four ply hot asphalt-asphalt saturated
organic felts. The roof system ideally must perform two main functions: (1) insulate the building;
(2) provide a weather barrier. The roof model is bounded by an internal space of constant air tempera-
ture and an external exposed surface upon which is imposed a sol-air temperature input.
3- Sol-Air Temperature Equivalent
The heat flow into a roof is due to the outdoor temperature 6 (t) and the incident solar flux l(t).
The rate of heat transfer q^ will be given by
q^(t) = h^(e^(t) - 6(0, t)) + al(t) (1)
where h is the surface conductance of the roof surface, 6(0, t) is the surface temperature at distance
of X = 8 and time t, and a is the solar absorptivity of the roof surface. This may be also expressed as
q^(t) = h^(eit) - 6(0, t)) (2)
o Ob
where 6^ is a fictitious temperature, the sol-air temperature and may be written as
9p(t) = 6 (t) + al(t)/h^ (3)
ho O
Since the surface absorptivity and outside surface heat transfer coefficient is contained in this ex-
pression, the relation is only good for a particular surface. A rather complex computer subroutine was
developed to automatically determine the sol-air temperature for any specified location, time of the
year, and for any given surface condition and orientation.
Figures in brackets indicate the literature references at the end of this paper.
670
h. Multilayer Periodic Heat Flow
Periodic heat flow through composite roof systems have been studied by a number of investigators,
Mackey and Wright [7] and more recently, Hoglund, Mitalas and Stephenson [6]. The present study employs
a computer program especially developed for determining temperatures and fluxes at any position within
a layered system and is a modification of an earlier program developed for making thermal diffusivity
measurements [8]. A Laplace transform was employed to convert the partial differential equation of
linear heat flow into an ordinary differential equation which was then solved in matrix notation form.
The input driving function at the exposed outer roof surface boundary consisted of the sol-air tempera-
ture expressed as a Fourier Series.
The tempera turCj^d i s t r i but i on , e^(x,t) within a given layer m of a multi-layer infinite slab of
total thickness L = composed of M layers of thickness L ,is given by the solution of the one dimen-
sional equation of linear heat flow with specified boundary condition,
a 6 (x,t) = e (x,t). ik)
m moo mt
The distance x is measured from the input face of the first layer. The thermal diffusivity, a of
each layer is defined as a = A /d C with A being the thermal conductivity: d , the density; and c"^,
mmmmm m m
the specific heat. It is assumed that each diffusivity is independent of position, time, and tempera-
ture. The subscripts, 6 and t, denote differentiation with respect to distance and time.
The boundary condition at the input face, x = 0 will be the sol-air temperature, e^(t) expressed
as a Fourier Series,
e^(t) = + I sin (27rnt + 6^) (5)
and
e (x,t)= 0 t 0 (6)
m
for all M layers. The temperature at the output face will be maintained constant at T^ for all time,
e(L,t) = T^ t > 0 (7)
In a multi-layer slab of M layers, an additional pair of boundary conditions is required at each
interface; namely, the flux and temperature must be continuous. At the interface between the m'th and
m'th + 1 layer, the boundary condition may be expressed as
m m
~ e ( iL ,t) = e ^, ( ,t) (8)
m y m m+ 1 | m
m m
X e AJl ,t) = A _^,e ^.Ah ,t) (9)
m m6 'j' m m+1 m+16 j m ^ '
This multi-layer boundary value problem can be solved by the use of the Laplace transformation
which converts the partial differential equation in G(x,t) to the ordinary differential equation in
u(x,p). The transformed equation for the m'th layer becomes
_ m- 1 m
u ..(x,p) - q'^u (x,p) =0 y L < X < Tl (4')
m66 '^^mm '^ ^m jm ^ '
2 ,
q = p/a
m m
The interface boundary conditions at the input face of the m'th layer transform to the form
m- 1 m- 1
I
1
Vl( K'P^ = ^m( ^m'P) (8')
m mS
I
m-1 m-1
f ,( ,p) = f ( [L ,p).
where f is the transformed flux.
( IL ,p) = XuA lL,p) (9')
m-, ,
671
The boundary condition at the final output face will be
u^(L,p) = 0
(7')
while the transform of the input boundary condition at x = 0 will depend upon the time dependence of the
input function.
The general solution for the m'th layer can be written in matrix form [8]
u
mo
^11 ^12
u .
m 1
u .
m 1
f
mo
^21 ^22
f .
mi
T
m
f .
m 1
(10)
where the subscripts o and i designate the value of the transformed temperature or flux in the plane of
the output or input face of the m'th layer. The terms in the square matrix are given by
T] 1 = T._ = cosh (q L )
11 22 mm
12
s i nh (q L )
^m m
\ q
mm
21
A q s i nh (q L )
mm m m
(11)
and T is the matrix for the m'th layer.
m
If layers from 1 to M are placed in series so that the output of the m'th layer becomes the input
of the m'th + 1 layer, the matrix equation becomes
"li
f , .
m=l
TT T
m=M
m
(12)
1 i
For a general position, x > measured from the input face of the m'th layer, the matrix equation is
(13)
m-1
where the arquments of the hyperbolic functions in the matrix T wi 1 1 be q x or q (x - Tl ) as x i s
mx m m m y m
measured from the input face of the first layer. The values of the input functions of the m'th layer
are given in terms of the output functions by
u
u .
mx
T
m 1
f
mx
f .
mx
mi
•1
f .
(I't)
where T is the inverse of T .
m m
Thus, the value of the function at x the m'th layer is given in terms of the output
mx
mx
mx
or in shortened form
mx
mx
mx
m=M
^Mo
^Mo
'^Mo
T-'
m
^Mo
T-'
m
^Mo
^Mo
(15)
(16)
672
Solving equation 12 for the input functions gives
^li
m=M
= TT
T-'
'^Mo
^li
ni=l
m
''mo
Mo
""mo
(17)
The ratio of the temperature at x to the temperature at the input face, x = 0, for a constant tem-
perature at the output face, x = L is given by solving eq 16 for u^ and eq 17 for Uj. and dividing to
obtain the desired ratio; i.e., '"^
u N,_
mx = _L2
^li ^12
Mo
''mo
u(x,p)/u(0,p) = N|2/D,2 = Z
(18)
The value of Z, the ratio of the transformed temperature at x to the transformed temperature at
X = 0, ^\2^^]2' ^ complex quantity dependent upon q, the thickness of the layers and their physical
properties. The expressions for e(x,t) and 8(0, t) are obtained from u(x,p) and u(0,t) by use of the
Inversion Theorem by which the residues at the poles of the integrand are evaluated. For the case of
the steady periodic state, only the residues at the poles which occur along the imaginary axis need to
be evaluated. For an input function containing a single frequency, w, these poles will be at -iu. Thus,
for a sine wave input function, Z is obtained by evaluating '^]2^'^12 ^'^^ factor q in each argument
given by q^ = ( i oi/a^) ■'•^^ . The vector Z gives the attenuation and phase lag of an input sine wave of
temperature when measured as a temperature at a position x in a multi-layer infinite slab.
For periodic input functions expressed as a Fourier Series, the application of the Inversion Theorem
on the transform of the temperature requires the evaluation of the residues at pairs of poles at ±inaj
where the values of n depends upon the harmonic content of the input function. The residues will be ^
given by A Z where Z is the value of Z with the factor of q of each argument given by q = (inoj/a ) •'• f
^'nn n ^^ ^m m
and A is the coefficient of the n ' th harmonic of the Fourier Series expansion of the input function
6(0, t^
The matrices N and D become unwieldy when used to obtain an explicit expression for Z of a slab
containing more than two or three layers. The matrices can, however, be evaluated by purely numerical
methods using complex-mode computer programs. When this method of calculation is used, each term in the
matrices N and D is determined with equal ease. It is thus possible to find a vector Z giving the ampli-
tude and phase lag of the temperature or flux at a point x with respect to a temperature or flux wave
incident on the input face of a multi-layer slab with the output face held in an isothermal or adiabatic
condi tion.
5. Design Objectives
As indicated earlier, a roof is to perform the major objectives, i.e., provide thermal insulation
for the control of the internal environment and act as a waterproof weather barrier. It should accom-
plish these objectives within certain economic design limitations. The total roofing system also has to
carry its own dead weight plus any live loading from wind, snow, rain or normal maintenance traffic.
The latter objective is generally the sole responsibility of the structural deck system. Certain types
of application may also require a fire rating for the roof system. In total, there may be as many as
five or six functions to be performed by a given roof system, and in most cases, there will be conflicts
between certain design objectives which will require some form of compromise in terms of the final design.
Determining the amounts and type of insulation to be employed within the confines of a particular system
can involve a number of considerations ranging from economic to thermal performance. A procedure for
performing mu 1 t i va r i ab 1 e optimization has been developed previously and is described in the following
section.
6. Basis of Optimization
The basis of the optimizing procedure is a generalized mu 1 t i va r i ab 1 e optimization criteria that
attempts to compromise design objectives and any inequality constraints. The procedure was originally
presented as a structural design aid by Gall and Krokosky [9]. Since every design is a compromise
673
between conflicting goals, each design reflects the designer's ability to perform some trade-off among
various goals. The present design program still requires the judgment and selectivity of the designer to
determine realistic perfor,mance indices. The determination of performance indices is by far the most
difficult part of the entire procedure. Variations of the procedure are limited only by the imagination
and resourcefulness of the designer. However, for the untrained designer, the determination of perfor-
mance indices can be developed heuristical ly .
7. Present Optimization Scheme
The current program specifically designs a three-layered composite roof system by selecting the
materials from a data bank of discrete material properties. The final design represents a compromise
between thermal performance variables and cost. The importance of each design objective is determined
by the designer in setting up the various performance indices into a so-called ranking matrix consisting
of levels of desirability.
8. Ranking Matrix
The heart of the present procedure utilizes a ranking matrix of system functions which reflects the
designer's ability to recognize and to assess the relevance and desirability of each design function.
Table I shows such an array for a typical roof design considered herein.
TABLE I
Design Ranking Matrix for Roof Section
Cost of
Insulation
Total
Integrated Flux
Maximum Peak
Thermal Flux
Max i mum Fe 1 t
Temperature Differential
($/ft^)
(BTU/ft^24-hr
. pe r i od
(BTU/hr/ft^)
(°F)
0.00
0.00
0.00
0
.00
0.25
50.00
10.00
25
.00
0.35
75.00
10.00
25
.00
0.45
100.00
20.00
25
.00
0.55
125.00
30.00
25
.00
50.00
150.00
300.00
300
.00
Limi ts :
Thickness (ft)
0. tl
0
500;
t^ = 0.; tj = 0.333
Density (#/ft^)
1 . 9 .< p , .<
27. 0;
^2 =
70.0; = ]k0.0
The matrix ranks system attributes against an absolute scale of performance. The first row, J = 1,
represents the most optimistic desires for the performance of the system as well as the upper bounds for
each system attribute. Row two, J = 2, gives the designer's appraisal of excellent performance and so
on down the following rows with each succeeding row having less desirable characteristics than the pre-
vious row. The designer can use as many rows as needed. In each case the last row is known as the
funnel row and its function is to funnel the performance characteristic within ranking considerations.
The only restrictions on the construction of such an array are that each row must contain values of
system attributes of equal desirability and each column in the array must be montonically increasing
or decreasing.
9. Search Procedure
The optimization search procedure relies on a pseudorandom or adaptive search techniques in which the
search probability is not fixed but shifts around as the search progresses. A purely random search pro-
cedure would use a probability density that is uniform over the whole search procedure. The search
relies on a probability density that is a maximum at the current best value of the design parameters.
In the present program, these parameters are the density of the insulation, conductivity and the corres-
ponding thicknesses of the insulation.
674
On each side of the current best value the probability density decays with some exponential value
of [odd integer - l)/odd integer]. A new choice of parameters is determined by
K0[I] = KB[I] + [ |uB[l] - LB[I] | R^] (19)
in which KO = the newly chosen search parameter; KB = current best value; LB and UB = the upper and lov/-
er search parameter bounds; R = a uniform probability density between -I and I; and 9 is the odd integer
describing the probability density decay. Every time a better point is found that results in a lower
value of J , its corresponding variables are stored in KB. The maximum value of all the desirability
ratings is given by J^, i.e.
J = maximum [RA[N]] (20)
m
in which N = the number of system variables and RA = the desirability of each system variable which is
obtained by linear interpolation of the calculated value and the design values from the ranking matrix.
Thus, figure 2 shows the flow chart for the ranking optimization program. In this particular variation
of the program, the density variable is used to select the materials for insulation. The random value
of the density is used in conjunction with the discrete material file. An interpolation is carried out
and the discrete material having the density closest to the pseudorandoml y generated value is then
chosen along with its properties for a given ranking. The program can be run for any given period of
time until the desirability of each system variable is approximately equal or until there is no appreci-
able change in the J value.
^ m
10. Inequality Constraints
The ranking array can be set up to act as an inequality constraint so that underdes i gned quantities
are the ones that are immediately reduced, see Table II. Underdes i gned quantities are fixed so that
they have a high J , therefore a low desirability, while the overdesigned have a low index and are not
usually reduced further.
Table II
Typical Ranking
Array Showing Implications
of Underdesign and
Ove rdes i gn
Des i rab i 1 i ty
Maximum Temperature
Des i rab i 1 i ty
Equivalent To
1 ndex
Gradient Across
1 ndex
Felts, °F
J[l] Most desirable
0
J[l]
Overdes igned
J[2]
25
J[2]
J[3]
25
J[3]
A 1 1 owa b 1 e
25
J[4]
J [5] Funne 1 Row
300
JL5J
Underdes i gned
II. Illustrated Example Application
Possibly the best method of showing the usefulness of the previously described analytical techniques
is to consider a specific example. The thesis previously expressed was that conventional roofing design
employing the built-up roofing waterproof membranes exposed to the weather was, in fact, somehow poor
des i gn .
The aforementioned thermal analysis and optimization procedure were applied to this particular prob-
lem in an effort to search out more desirable designs. Specifically the present design considers the
implications of placing the built-up membranes under the insulation.
Initially only four major parameters were considered in the ranking matrix as shown in Table I.
These were the cost, total integrated flux, maximum temperature differential of the membrane layer, and
maximum thermal flux transmitted through the roof section. TJne inclusion of cost as a comparative param-
eter is obvious, whereas the other parameters may not be as obvious. The temperature differential of
the felt membrane layer was considered for protection against thermal shock and excessive thermal cycling.
Finally, the peak thermal flux was considered to give some indication of the overall thermal design of
the roof as far as the interior environment was concerned.
675
Initially the search was also limited to six specific insulations as shown in Table III. Other
insulations or variations of insulation properties with density could have been included as well, but the
present study was purposely kept simple so that the overall approach could be emphasized.
The object of the present search was to select the most economical insulation, and thickness of in-
sulation, from the possible insulations listed in Table III which would also satisfy the criteria of the
ranking matrix, Table I. Allowable insulation thicknesses are also shown in Table I.
Table III
Material Properties
Material Density Thermal Conductivity Specific Heat Cost
#/ft^ BTU-ft/hr.°F-ft^ BTU/lb/°F $/Board ft.
Urethane 1.9 0.012 0.21^0 0.17
FOAMGLAS 9-0 0.033 0.185 0.15
Aspha 1 t-coated
lightweight 15-0 O.O38 0.200 0.08
aggregate
Fiberboard 15-1 0.030 O.5OO O.O7
Lightweight
aggregate insul- 25-0 O.O58 O.I69 0.08
ating concrete
Cone rete-coa ted
lightweight 27.0 O.O65 0 . 1 80 0.10
agg rega te
Built-Up Roof 70.0 0.093 0.370 0.22
Concrete 140.0 1.000 0.210 0.05
The specific climatic conditions considered in this paper correspond to a site just east of Pitts-
burgh, Pennsylvania"". Both a representative summer and winter day was evaluated. Specific information
concerning dry bulb air temperatures, cloud cover, wind velocity, etc. was chosen to be representative.
In the present program, any region of the United States could just as easily have been considered.
11. Results
Summer, Case I - (Concrete structural deck) + 4 ply membrane + Insulation. The first example con-
sists of conventional k ply built-up roofing membranes placed over four inches of structural concrete
deck and subjected to a typical summer sol-air temperature driving function as shown in figure 3. To
begin the search, a guess is made as to the yet unknown insulation and its thickness. Initial values of
system object functions are then calculated and compared to the allowable limits. If the values are all
within the limits, each function is then ranked according to the ranking matrix shown previously. The
next cycle of the search then attempts to improve the rank of the worst ranked parameter by either a
change of insulation thickness or insulation material.
Shown in Table I V-A are actual ranking output generated by the program for which several improved
ranks were found. It can be quickly seen that the initial estimate was unsatisfactory in terms of the
total heat gain, (i.e., rank k-2'ik). It should be remembered that the more desirable the function, the
lower the rank value will be. After only slight improvement was achieved by an increase in thickness,
the search procedure shifted to a lighter and more efficient insulation. In so doing, the cost then
became the critical parameter and further searching ultimately produced a design where the cost and total
flux were of approximately equal rank and the search was terminated.
.................................. J
676
Table I V-A
Optimization Search Output
A. Summer Condition - Concrete Decl<.
Design Parameters and Rank
Current Insulation Choice
Max i mum Fe 1 1
Den s i ty
#/ft^
1 11 1 \v l\l 1 C O 3
Ft.
Cost
$/ft^
Tota 1 F 1 ux
BTU/ft^/2'4 hr.
Peak Flux
BTU/ft^/hr.
Temp . Differentisl
°F
25.0
0.210
0
202
105.85
7
75 1
8.888
(1
806)
[ ^.23k]
(1
775)
(1 .355)
25.0
0.217
0
208
103.61
7
559
8.6^49
(1
833)
[ ^.l^t^t]
(1
756)
(1 . 3^*6)
9.0
0.217
0
390
68.30
k
859
5.397
[3
^402]
( 2.732)
(1
it86)
(1.216)
9.0
0.
0
355
73.58
5
266
5.899
[3.046]
( 2.9^*3)
(1
527)
(1.236)
Table IV-B
Optimization Search Output
Winter Condition - Concrete Deck.
Current Insulation Choice
Design Parameters and Rank
Max i mum Fe I t
Dens i ty
ff/ft^
Th i ckness
Ft.
Cost
S/ft^
Tota 1 F 1 ux
BTU/ft^/24 hr.
Peak Flux
BTU/f t^/hr.
Temp. Differe
°F
9.0
0.210
0
378
145.37
7
863
5
.560
(3
28)
[ 5. 815]
(1
786)
(1
.222)
1 .92
0. 172
0
102.29
4
578
1
.21
(3
009)
[ 4.092]
(1
458)
(1
.049)
1 .92
0. 179
0
y8.82
4
421
1
.169
13
147)
[ 3.953]
(1
442)
(1
.047)
1 .92
0.213
0
84.36
3
772
0
.983
[3
846]
( 3.374)
(1
3/7)
(1
.039)
All system attributes were not equally ranked because the original ranking matrix tended to over-
design the peak flux and maximum temperature differential for the present input function.
Winter, Case I - (Concrete structural deck) + 4 ply membrane + Insulation. Since most of the north-
ern latitudes of the United States experience a great difference in ambient outdoor temperature from
Summer to winter seasons and any insulation system must function year round; real designs would have to
consider more than just one input sol-air condition. Although more elaborate design criteria would un-
doubtedly be considered in an actual design, for the sake of demonstration and comparison, a typical
winter sol-air temperature was developed for the same roof and location as in the summer case just dis-
cussed. This sol-air temperature shown in figure 4 was used as input to the optimization program and a
new search was made for the optimal insulation to function under winter conditions for the same design
criteria as given in the ranking matrix of Table I.
677
Table IV-B shows the actual ranked designs for the winter input. It is seen immediately that what
was the best choice of insulations for the summer sol-air conditions no longer was acceptable because of
the large heat loss shown as total flux, i.e. Rank, (5.815) • The next ranked design shows the effect of
a lighter and more efficient insulation, but again a more costly insulation. This is reflected in a
shift of the critical parameter from total flux to cost. Further searching produced a slight reduction
in the cost rank by reducing the thickness.
It is interesting to note that the optimized designs for summer and winter conditions do not suggest
the same insulation in each case. The summer design uses 2.36 inches of 9-0 pcf density insulation and
the winter case selects 2.56 inches of 1.92 pcf density insulation. In a real case an additional criteria
such as the cost of heating and cooling could be included to aid in the decision. The addition of such
a criteria in the present program would present no serious problems.
Figures 3 and h show computer-generated data for both the sol-air equivalent driving functions and
the responses of both the protected and conventional membrane roofing systems when insulated with the
designed winter insulation. It is at once obvious that the protected membrane system effectively damps
out the large thermal fluctuations of the driving input sol-air temperature and provides a relatively
stable thermal environment. The conventional designed membrane on the other hand very closely tracks
the input sol-air temperature. The conventional membrane curves and sol-air temperature are shown as
a single line because the membrane temperature is so close to the input.
Since the initial example consisted of a rather massive structural deck, i.e., 4.0 inches of con-
crete which provides the potential for a large amount of heat storage, it was decided to test a second
example with a vastly different deck construction. The second case consists of a corrugated metal deck
and a 0.5 inch layer of fiberboard adhered there unto as a base for the built-up roofing membranes.
Once again the task was to determine the type and thickness of insulation to protect the membranes and
to provide the major insulation for the building for both the summer and winter conditions.
Summer, Case II - (Corrugated metal and fiberboard deck) + k ply membrane + Insulation. Table V-A
shows the resulting ranks for both the initial
tion, and succeeding generated values.
estimate, i
2.52 inches of 25.0 pcf density insula-
Table V-A
Opt i mi za t i on
Sea rch
Output
S umme r
Condition - Steel
Deck + Fi berboard .
Current
nsulation Choice
Des i gn
Parameters and Rank
Cost
Total
Flux
Peak
Flux
Maximum Felt
Dens i ty
#/ft^
Th i ckness
Ft.
$/ft^
BTU/ft
^/2k hr.
BTU/ft^/hr.
Temp. Differential
°F
25.0
0.210
0.202
84.
51
1 1
273
29.711
(1 .806)
( 3.
380)
( 3
127)
[ 5.017]
9.0
0.217
0.390
57.
83
7
806
20.587
[3.'t02]
( 2.
313)
( 1
781)
( 1.824)
9.0
0.197
0.355
61 .
73
8
376
22.098
[3.046]
( 2.
469)
( 1
838)
( 1.884)
15.0
0. 197
0. 189
67.
52
9
032
23.809
(1 .756)
[ 2.
701]
( 1
903)
( 1.952)
Initially, it is seen that the membrane temperature differential was the critical, or worst, ranked
parameter. Attempting to correct this, the cost then became the decisive parameter. Finally the search
procedure settled on a compromise insulation where total flux transmission was the critical variable.
At this point time terminated the search procedure and it can be seen that three of the four ranked
parameters are approximately of equal ranked value. Had time not terminated the run, it is most likely
that the thickness of insulation would have been increased, increasing cost slightly, while lowering
total flux, peak flux and maximum felt temperature differential. The cost and total flux would then
have been of approximately equal ranking magnitude. It is somewhat interesting to note that with this
678
lightweight metal deck system there is an increase in the maximum felt temperature differential over
over that observed with the more massive concrete deck system. The mass of the concrete tends to pro-
vide inertia which resists the rapid input fluctuations.
Winter, Case II - (Corrugated metal and fiberboard deck) + h ply membrane + Insulation. Once again
the second part of the procedure was to evaluate the search for the winter sol-air temperature input.
Table V-B shows the results from the optimization search. Initially the total flux, i.e., heat loss,
was the critical parameter with a rank of [5.261]. The search procedure improved on this rank by
switching to a more efficient insulation which also increased the cost. Further searching reduced the
cost somewhat but not enough to remove the cost as the critical parameter. As in the former case, a
different optimum design is suggested for the winter case as compared to the summer condition.
The input sol-air temperature and system thermal response are shown for both summer and winter con-
ditions in Figure 5 and 6. As with the previous example, the insulated or protected membrane remains
essentially isolated from the large input temperature fluctuations although as noted earlier, the pres-
ent case does show somewhat larger fluctuations than the concrete deck system.
Table V-B
Optimization Search Output
Wi nter
Condition - Steel Deck
+ Fiberboard.
Des i gn
Parameters and Rank
Current
Dens i ty
Insulation Choice
Th i ckness
Cost
Total Flux
Peak Flux
Maximum Felt
Temp. Differential
#/ft^
Ft.
$/ft2
BTU/ft^/2i( hr.
BTU/ft^/hr.
°F
9.0
0.210
0.378
131 .52
8.739
21 .085
(3.28)
[ 5.261]
(1 .87^*)
{ 1.843)
1 .92
0.210
0.it28l
81 .i)7
4.033
4.695
[3.781]
( 3.259)
U .403)
( 1.)
1 .92
0.207
0.
82.39
4.078
4.749
[3.725]
( 3.29b)
(1 .408)
( 1.190)
12. Conclusions
Although we have not had enough experience with the present program to be able to state generali-
zations regarding the design of protected membrane roofing systems, we feel the present approach will be
extremely useful toward that eventual end. We believe it is significant that seasonal demands caused by
different sol-air temperature driving functions dictate different insulation requirements for summer as
compared to winter conditions. The present example has shown the benefits to be derived in terms of a
stabilized thermal environment for the membrane in a protected membrane roof insulation system indepen-
dent of seasonal conditions.
The present multifunctional optimization program offers the design engineer an efficient means of
assessing the effects of variations in specific design parameters on the overall design of a building
material system.
We feel that it is especially useful in discovering and resolving the conflicts between the various
design criteria which do arise in multifunctional systems. The designer can then easily determine the
degree of interplay and the limitations of design variables. The need for rational compromise is then
made more apparent.
Since the most difficult part of the design process appears to be the specification of equivalent
desirable performance criteria for the many variables involved, it is also possible to use the present
program as a heuristic design learning process for the actual establishment of said performance
cr i ter i a .
679
680
DES IGNATE
UB, LB [l];
KB
J MAX 10--'--
RANNO ^- K0[I] ^- KB[l] + ((UB[l] - LB[l]) * (RANDOM4 9))
K0[I]
K0[I]
LB[I]
UB[I]
NO
_1
YES
RELATIONSHIPS BETWEEN
SYSTEM VARIABLES &
DESIGN PARAMETERS
XO[C] ^ □ - K0[I]
RANNO:
PSEUDO:
RANK XO [C ]
XO[C] >
J0[5,C]
COST, ETC.
1
4 F
DETERMINES DESIRABILITY INDEX
RA[C] XO[C]
JMAX <
RA[C])>-
ALL SYSTEM VARIABLES
RANK XO[C]
FLUX
XO
[C] > J0[5,C] T^
DETERMINE DESIRABILITY INDEX
J[C] <- X0[C]
equal number of system
pa rame te rs
initially any va 1 ue will
time limiterwill end
p rog ram
JMAX
LC, D,J
(6)
If there are heat sources cHt^=H(,exp( jwt ) (k=2,,..n) at the each boundary, eq (5)
bee omes
Q
A B
+ 21 .-^
A, B,
Bk
(7)
v?hich
n
TT
•n
TT
Ate Bk
A„ B„
1 0
0 1
(8)
However, I will explain for the case, H=0. Each four terminal matrix of v/all
has the next property. (^i?}
A B
C D
= AD-CD =1
(9)
From the property on the product of determinants,
An B
A, B,
C, D,
An Bn
Cn Dn
|A, B,
ICi D,
(10)
Substituting eq(9) into eq (10), we have also the follov/ing property for the
multi-layer wall.
A B
C D
An. Bn
Cn Dn
A, B
C, D|
= 1
(11)
As an another form of the matrix, we can obtain the following equation by using
eq (5).
696
c9n
Ji^ii Y^v
(12)
where
Y --^
^" " B '
y AD - CB
Ya, =— = Y.
B '
(15)
and the matrix in eq (12) is named admittance matrix in electric engineering.
It must be noticed that the direction of the heat flov; v;hich flows from the
surface n (or the surface 1 ) to the surface () is determined as the plus direction
for eqs (1),(4),(5) and(7). On the other hand for the eq.(12) direction of heat flow
which flows into the inside of the wall from tt^e surfaces is determined as the plus.
5.2 I'lulti-layer Wall + Semi-infinite Wall
Relation between c&, and cQs which are the temperature and the heat flow at the
surface of the semi-infinite wall is expressed as
(14)
Where ,
Z =
(1-j)
(15)
'When a multi-layer wall, vrhose elements of the four terminal matrix are A, B, C
and D, is adjacent to a semi-infinite wall, the relation between cBn, c&s and Jin, cQs >
which are the complex tem.peratures and heat flov;s of the surfaces of the multi-layer
wall, are expressed as follov^ing by using eq (6).
tQr.
A B
C D
(16)
Substituting eq (14) into eq (16), v;e obtain
= A + B ,q
(17)
697
so that
1
A + 2
TtT^-^'^ ^^^^
Z A + B •
Frora eq (16), we have
d3n= C ces+ D cQs
= ( C+-|-).0, . (19)
Substituting eq (18) into eq (19), we have
ZA + B Z
- ZC + D o
ZA + B
= Ym c8,v, (20)
where Y„- ^2,
ZA + B
(21)
4. Heat Balance Equations for A Multi-room Building
Now we obtained the thermal properties of the v/all in the four terminal matrix and
the admittance matrix. By using these matrices the system is expressed also in the
matrix equations.
4.1. Heat Balance Equations for Each Room
Let ki be the room which is adjacent to the room i. When we express the elements
of the admittance matrix of the wall, which exists between the room i ani the room k^,
by Ytei^inYk;-i2.»Yte.~2i and Yr;~xx , the heat flow cQm^tei , which flows into the room i
through the wall v/hen the temperature of the room i, ^8; , is zero and the temperature
of the room k; is cQk,, is expressed as follovang.
On the other hand, when Sk; equals zero and c®i is not zero, the heat flow which
flows out from the room i is obtained by
698
And the heat quantity cQ^-l v/hich is stored in the heat capacity of the room i,
Cm-i , depending on the temperature fluctuation is expressed as follows.
cQc~i — Ca-i
dt
(24)
Expressing the heat quantity by sign cHi which is supplied into the room i, and
another knovm heat quantity in the room i by the sign cQ; , then v/e have the heat balance
equation for any co , as following.
(25)
By expanding the temperature and the heat into the Fourier series, which have m
terms, eq (25) can be vrritten as following.
m.
If there are ventilations G^(.t) from the room kc to the room i and Gj^.(t; from i to
k;, eq (26) becomes eq (27).
f [^Hc^i + cQ,.j] =fl(^Jc^,^,o~i +^G;^ (t) + jw^C^.. )cer.i + 2:(Y(,,,.,,).^+6r,,(t))^6j^_J (27)
4.2. Heat Balance Equation of Multi-room Building (1)
( General ^^at^ix Expression )
For the room 1, eq (27) becomes
for the room 2,
for the room n.
Vie can write eq (28) as follov;ing matrix form.
699
(29)
where Aj^ is the complex number matrix which is determined by admittances, heat capacity
of the room air, and where G(t) is time variant matrix determined by the ventilations,
and , ^©.^ are the supplied heat and kno^/m heat respectively.
4.5. Heat Balance Equation of Multi-room Building (2)
( Tri-diagonal Matrix Expression )
When we divide the system into three blocks as shown in figure 1 , for the block
1 the heat balance equations are expressed as follows.
lAii c0i, + ,A,i c0,x + ,Rm cBzi = cHi, + cQii
1A21 c©,, +,A«c®ii + lAj, ,6,3 + |Ri, c0!.i + .R>^ cSii = cHu + cQ,z V
.An c0,a + .A53 c0,3 + iRncOjj = cH,3+eQ,3 J
(50)
Equation (50) is expressed in the following matrix equation.
',A„
,A,x
0 ^
' .©„ ~
iR(i
0 ^
,A„
,Aix
1A23
+
,Rz,
. 0
lAjz
1A33,
.0
,Rji,
(51)
In the same vray, for the block 2 the matrix equation is
2.L11 iLi2. 0
^ 0 2L21 iLij
, <0r3 /
'lA,, zAu^rA,
iRu zRij 0
0 ^Ri. .R^5,
C033
(52)
and for the block 5,
'?L„ 0
. 0 jLjz.
C0J.I
3A,, jA,. 0
jAii jAzz jAij
0 sAsi 3A33j
' C031
, t033/
. CH33
(55)
Getting together these three equations, we obtain the following matrix equation.
700
'lAii lAii
I All 1A22
1 0 .A„
[2X111 zXlll
,A:
i:
0
0
0
0 ■
1
,R2I
0
(R32,
An
zAii
r
jAj,
lAai
I
3LII
0 '
0
3L?2j
3A.I
0
0
tl
0
.R.
jAiJ
0
0
0
0
0 1
jAii jAj3
jAji jAj3
til II
f
' n ~1
cyii
tQii
fcHail
+
(34)
vrhere L, A, R are complex coefficients which are determined by the admittances of
the walls and by the heat capacities of all rooms, and Sii is the temperature of the
room (i,j), cHJ is the supplied heat, and cQii is the known heat in the room (i,j).
By using the minor matrices A, L, R, 0 and the vector expression, eq (34) can be
described as following.
A, R,
L. A.
N
+
/
[ 003 J
(35)
If there are air flov/s between rooms, eq (35) becomes eq (36).
fA, R, 0 N
Az R:.
lo L, A3
G„
Gil 0
Gil Gi
Gji G3
f'®0
'cHi^
fcQi>
£ Hi
.C0B
. 'Hi J
(36)
Equation (55) and eq (36) are tri-diagonal matrix equations,
be obtained for the general multi-room building.
Same expression can
4.4. Heat Balance Equation of Multi-room Building (5)
( Transition Matrix Expression )
Though it is possible for the general multi-room building to obtain the transition
matrix expression by using eq (56), here I will explain the case of the one-story house
which is built in the grid type. Assume that there are j rooms (j=1,.,,nx) in the
direction x and i rooms (i=l , . . . ,ng-) in the direction y in the house.
The following signs are adopted here.
wall between a room(i,j-l) and a room(i,j)
vrall between a room(i-l,j) and a room(i,j)
floor of a room(i,j)
roof of a room(i , j )
room temperature of a room(i,j)
thermal capacity of the air in a room(i,j)
supplied heat in a room(i,j)
knovm heat in a room(i,j)
heat flow into a room(i,j) from another room(k,j) when
c@ii.O and c&^^O
heat flow from a room(i,j) towards another room(k,j) when
=0 and c®,^ kO
heat flow into a room(i,j) through wall jXi+i depending on
the room temperatures, tOij. and c&ii.*-\
heat flow from a room(i,j) through wall ^x; depending on
ce.-^ and t^ii-^
t^ii^\2 jYii-^iz
elements of the admittance matrix of wall
701
(1) Heat Balance Equation of the Wall x
For each v;all iX^^ the follov;ing equation exists.
Q'
(i=l,...,nM)
(57)
Expressing as follov/s,
f40
■ " 1
0
(c
s
0
0
k
7
H- =
0 B
0
Dn
>
(38)
By using eq (58), eq (57) becoms eq (59)
(59)
(2) Heat Balance Equation in the Room(i,j)
The total heat flow c% v/hich flov;s into the room(i,j) is given by the following
equation.
On the room(i,j) the follo\\'ing heat balance equation is obtained.
(40)
X,Hr^. +,Q,, +,H„ +,H?^ = 2:,Q^ +.Qe,.-;
Rearrangeing the eq (41), we obtain the following.
(41)
Hi
=2,q;^+.Q4 +.Q..i, -.Q., -cH., -2cH,, ,
(42)
in which cQii^ and cH^ are expressed as follovra by using admittances of the wall y,
702
and
cH,^ = Yi^^a c% ( l=i,i+l; k=i-l,i+1) ,
(43)
(44)
Substituting eqs (43) and (44) into eq (42), v:e obtain the follov.dng equations,
for i= 1 ,
for i=2.
cHJ^ =cQ.'^ + (Y.^.„ +Y5,.,, +>Co..,^) c0.; -Y,;.,2C05i -Y.^.^,c0.i - C0., - cH.; V(45)
for i=nj ,
Equation (45) can be ivritten as the following matrix equation.
J
Tj;,jj 0
(46)
where
'-i-kk =Yfej-.ii +Yte+,^.ij^ +j'"Ca^|,_^ (k=2, . , , ,n^ -1 )^
(k=2,...,n^) ^
(k=l,...,n3-1).
y (47)
Equation (46) is simplified as following.
(48)
Where
Tj:-i2 ^^*i3 '
Tj'-.i4 Tj^22 T;»2j
(49)
703
(3) Transition Matrix Expression
Substituting eq (48) into eq (59), we obtain the follovrings.
_ r(A. +B^T^-, ) c0,-, +B, cQi-, 1 _ [Bi ( cH,.,+ .Q,., )
- L(C^ +Di T,_, ) ,0,-.. +D, .Q'_, J I^D, ( .H^.,+ ,Q,., )j
_rA, +Bj Tj_, B,| r 0.-,] +rBj) (-cH^.,
(50)
(51)
By using the eq (51), eq (50) can be v?ritten as,
(52)
Connecting the eq (52), v/e obtain the followings.
For j=T
A. B,[(c®»
c, dJUq;
(53)
for j=2
B^
D.J
c n 1
(54)
finally for j=
D '
(55)
In which, let
]V I Ai' Bjl _ fA„ B«7
(56)
704
and
1 0
0 1
(57)
Equation (55) is the same expression as eq (7) for the multi-layer wall which has
the heat sources at all boundaries.
Transition matrix can be v/ritten as follov;s.
{M '4 - [
ki +BiT/-, B,
Cj +D, Tj-, Dj
B^r 1 0
_ rk, Bnr 1 0]
(58)
If there are no ventilations between the rooms which are laid in the x direction
( direction of heat flov; Q' ), the follov.dng result is obtained.
Aj Bj
A, 0
A. .
0
0
IfB,
D, 0 ^
[aXd] - tcJfBj
[a d) - [C B]]
(a D - C b]|
A,D, - Ci B,
A,D.- C.B.
0
o
In the same way v/e obtain
So that
= 1
(59)
1 0
= 1
(60)
Aj
B,
- 1
B,|| 1 0 1
1
dJITj-, 1 1
= 1
(61)
705
The property given by eq (61) is the same of the four terminal matrix of the wall.
By this property it becomes very easy to obtain the inversion of the transition matrix.
Even if there is no x vrall, v;e can treat the system as if there is x wall by
considering an imaginary v/all, v;hose elements of the four terminal matrix is as follows
A=D=1, B=C=0
5. A Calculation Method for the Intermittent Heating
By using eq (29), ^'hich is the general expression for the m.ulti-room building, I
will explain the calculation method. Let G(t) be zero. The calculation method for
G(t)=^() is presented in the next chapter.
Since G(t)=0, eq (29) can be written as follov;s.
x[Aji:0j=xj[.H,}4.QOj (62)
Let t the time during v;hich the heat flow h is supplied in the room, dividing t
into m and I express the heat quantity at the time k by h^ ( k=1,...,m+l ).
Nov/ the unknovm heat h is approximately expressed in arbitrary function by using
these unknovm h^ ,and then the function is expanded in the Fourier series as follovring.
h=r(£'a^^j^ )cosu;(,t+ z;(2.'b^^^^ h|, )sinujjt (65)
From eq (63), v;e obtain
cH=2:x(a^.^j -jb^^) h'^ exp(jaj£t). (64)
For each uj^ v/e can v/rite in the matrix form as follows.
[cHj] =z[a^^^ -jb^^i^J h^exp(jtu^t) (65)
Considering cQc =Qeexp( iioet ) and substituting eq (65) into eq (62) we have eq (66),
then by multiplying the eq (66) by the inverse matrix TA,;] ', v/e have eq (67).
e
[Aj3[,0e) =:sz[a5^(, -jbi.^,3 h;,exp(ju;jt)+2:[Q^]exp(jw;j^t) (66)
U^l] =f^^l^l h;jexp(jaJit)+r[Ae][Qjexp(ju;gt)
= hw)^xp(ju;^t)+2:[Q']exp(ja;,t) , (67)
706
where
(68)
Let
then, from eq (67) the real function 6j can be written as follows.
9^=n(t,Re^^ cosLOjt-hliL^i, sincojt )h|^+ ^jcos oogt- sinoogt (69)
Let 6 be the given temperature from time ti to tz, then the unknovm heat
quantities h^ are obtained by solving the simultaneous equation which is gained by the
following equation.
9
-J(©-| e/dt= ^|l.®"ft^'^ kRj-f^'COS wjt- i;[j^^'Sinu;jt)h>^R5Cos«jjt-<^I^sinu;^t|dt
= j |^^|e-s:Cz(^Rj^^-cosu;jt- J^^i^.sinujjt )h'^'+ ^R^cosu^^t- .^Ij sinu>jt)| Jdt
"t| ^ ^
= 2 jp-z 2(tiR5^^. cosujjt- i^IiL~te'Si^'^4*)'^te'+'^f^?°°S"^e*~|I(i sinu^^tj
x[ i:(KRt.^„ coscojt-i^I^^^^ sinu5^t )jdt
= 0 ( k=l, • • - ,m+l ) (70)
6. An Expression for an Iterative Method
The number of unknovms of eq(70) which is expressed for a multi-room building
generally becomes too large, then it is not advisable to solve the equation directly.
Moreover for the case G(t)#0, it is very difficult to obtain the analytical
solution for eq (70). Then, here, as a practical procedure an iterative method is
explained.
We write again eq(29),
^{[aO +(G(t)]j j;,ej= ^{(cH,} + isi,]] (71)
Divide the matrix (A^] into the two matrices as follows.
707
' -^l-ii ^l^a • ■
^t-ll ^t-li ■ ■
h-ii ^s-ji ^t~i3 ■ ■
Ao,
L : '. 0
(72)
The first terra at the right side of eq (72) is a diagonal matrix and the all
diagonal elements of the second matrix are zeros.
Substituting eq (72) into eq (71), v/e obtain
2:
0 Ae.iz
G„(t)
= z
(75)
The iterative procedures are carried as follows by using eq (75).
Procedure 1. Let the mean ventilation rates be the approximate rates, and then
assume that the room temperature to be determined is equal to the adjacent rooms.
By these approximations eq(75) becomes the follov/ing.
''Aj^i +G,
= Z.
+ z.
{
a
(74)
in which
and T is the time of one period.
Gi =
(i=1,...,n) ,
^Jj-^]G,-^(t) dtj (i=l,...,n) ,
(75)
(76)
Thus the coefficient matrix of eq(71) results in the diagonal matrix, then we can
obtain the each room temperature and heat to be vSurpclied in each room independently
by eq(74).
After the procedure 1 , the follov/ing procedure is repeated untill v/e obtain the
satisfactory results.
Procedure 2, Let the temperatures ©• obtained already be the temperatures of the
adjacent rooms and assume that the matrix G(t) is multiplied by the temperatures 0'.
By this procedure eq (75) becomes eq (77).
0
A«^n
+
+
)
I
-G(t)
(77)
708
In eq (77), the^ vector c&' is knovm, then we obtain the follov/ing.
0
= H
+
0"
Q"
= 11
+
1
(78)
where
and
Qir
■Ac.
r a' ^
0"
-G(t)
.Qa.i = cQiM + cQt.c + ^Q^l; (i=l,...,n)
(79)
(80)
Equation (78) is also the diagonal matrix, so that we can determine the unknown
heats to be supplied and the room temperaturs of the each room independently. We repeat
the procedure 2 untill 0' becomes nearly equal to @.
7. An Example
An one-story concrete house vras taken as an example ( figure 2), and the following
quantities were calculated.
1. The room temperatures 9n, which are formed when the outdoor temperature (i=1,
...,6) are those as shown in figure 3 and there are no supplied heats in the house.
2. The heat quantities H,v7hich are to be taken off from the rooms to form the
room temperatures excepting corridor in 25°C from 9 am. to 5 pm. .
5. The room temperatures 6c, which are formed when the heat quantities H are taken
off from the rooms excepting corridor.
For numerical calculation temperatures and heat quantities were expanded in the
fifteen terms Fourier series ( w, , co^, u?,, . . . ju;,^) .
Unknown heat quantities H v/ere divided into five parts and approximated as the
broken lines respectively.
The sol-air temperatures 0j-£(i=1 , . . . ,6 ) in the figure 3 act against the east, the
west , the south, the north walls, the roof and the floors respectively.
The results of calculation are shown in figure 4.
It needed four times calculations for each room to obtain the satisfactory result.
709
8. Conclu'5ion
By using the frequency tran??fer function, three kinds of matrix equations whose
elements are complex v/ere expressed for the multi-room building.
The first one is expressed in the general matrix form of the simultaneous equation,
the second is the tri-diagonal matrix equation v;hose elements are consist of the minor
matrices, and the third is the transition matrix equation.
The tri-diagonal matrix expression reqires the less amounts of the memory of the
computer than the general matrix expression. The transition matrix expression for the
building is similar to the four terminal matrix expression for the wall. Therefore we
can say that the four terminal matrix is only a special form in the transition matrices.
This expression is especially usefull when we vrant to know the relations between
some tv;o blocks in a building.
It was introduced that the determinant of the transition matrix is unity as same as
the determinant of four terminal matrix. By this property that the determinant is unity
it becomes very easy to obtain the inversion of the transition matrix.
A calculation method for the intermittent heating, depending on the Fourier
analysis, vras presented.
As the practical procedure, an iterative method vras proposed. For an example
at first the heat quantities, v;hich are to be taken off from the each room to form the
predetermined room temperatures, v;ere determined, and then the room temperatures were
calculated for the obtained heat quantities.
As sho™ in figure 4 arround 9 and 17 o'clock there are comparatively large
differences between the predetermined and the determined temperatures, but at the most
of the time they are in good agreement.
Of course more detailed research is necessary for the method proposed in this paper,
but from these results it seems to be quite all right to consider that this method is
useful for the some problems such as the thermal planning or dicision of zoning.
9. References
( 1] Maeda,T. Theory on the room temperature variations. Trans, of Architectural
Institute of Japan (A.I.J) April (in Japanese)
L 2j Maeda,T. Theory on formation of the predetermined room temperature variations,
Trans. A.I.J. Sept. (in Japanese)
[ 3] Fujii,S. Temperature variation in the concrete buildings, Trans. A.I.J. No. 65
Oct. (in Japanese)
[ 4) Hasegawa,F. Analysis of room temperature. Trans. A.I.J. No. 64 Feb.
(in Japanese)
[ 5] Akioka,M. The theory of transient room temperature for intermittent heating,
ventilating and air conditioning, Journal of the S.H.A.S.E. Vol.41
(in Japanese)
[ 6J Ochifuji,K. Analytical method of transient room temperature in multiple rooms.
Technical Report of Hokkaido Univ. Vol.46 (in Japanese)
[_ 7j Aratani , Sasaki and Enai, Successive integration method for the analysis of room
air temperature or thermal load variations, Technical Report of
Hokkaido Univ. Vol.51 (in Japanese)
[ 8^ Nakazavra,Y. A calculation method for room temperature, Trans. A.I.J. , Extra, Oct.
(in Japanese)
C 9] Maeda,T. A calculation method for periodic room temperature variations in the
grid type building. Trans. A.I.J. NO. 49 Oct. (in Japanese)
[10} Eguchi,K. Theory on the room temperature variations and heating loads. Trans.
A . I .J . ,Extra , Aug, (in Japanese)
[1 1} Yamazaki,H. A calculation method for heating loads, Trans. A .I.J. , Extra, Aug,
(in Japanese)
(12} Nakazav;a,Y. Theory on the room temperature for intermittent heating, Trans, A.I.J.
Extra, Aug, (in Japanese)
(15) Carslaw and Jaeger , Conduction of heat in solids, Oxford,
710
(1.1)
ROOM
(3.1)
(1.2)
(3.2)
(2.2)
(1.3)
(3.3)
BLOCK1.BLOCK2.BLOCK3.
Fig 1 Block Plan of a Building
N
5M 5M 5M
' 1
1
ROOM
2
3
(
CORRIDOR
6M
3M
2.5M
Fig 2 Plan and Section of a Model Building
711
713
1
An Bxample of Heating and Cooling Load Calculation Method
for Air-conditioning of Building by Digital Computer
Shoichi Kuramochi
Taiaei Construction Co., Ltd., Tokyo, Japan
Today, many air conditioning engineers recognize that the actual load for air
conditioning system can hardly be achieved by the conventional heating and cooling
load CEdculation method. In , the author worked out a load calculation system,
in which the numerical ceilculation method was adopted to solve the problem on heat
transmission, and has finally perfected this calculation system for actual use
quite recently. The characteristics of this calculation method can be summarized
as follows: The air conditioning system in Japan is in majority operated intermit-
tently in a day and quite particular phenomena appear during the early hours after
the commencement of operation and right after the termination of operation. These
phenomena are caused by the transition of heat retained by the building and air
conditioning system as heat capacity. The calculation method worked out hais
advantages over the others in representing the phenomina mentioned. To be more
specific, while any physicail system doesn't particularly need to be conditioned
linear or invariable for calculating heat transmission, the storage heat load can
be accurately ccQculated by use of this calculation method. Moreover, this calcu-
lation system is marked by its reliability in securing an accuracy within the al-
lowable degree for load calculation. It also permits easy understanding for the
practice engineers in general, hence it will be widely useful for the professional
engineers. Improvement and modification to this calculation system can be also
made without much difficulties. This calculation system is mainly composed of two
parts, namely,
1, the calculation for obtaining the outputs of the heat source equipment
of air conditioning system, and the heat transfer rate of thenml medium
transportation syston and the changes of room temperatures, and
2* the calculation for the heating and cooling load changes in the air-
conditioned rooms.
In the text of this report, the equations adopted for this calculation are
firstly illustrated, then the formation of the calculation system is explained in
detail and lastly the results of the calculation made for the model building in ex-
istence are checked and assured by carrying out the actuail meeisurements and by com-
paring the measured values with the values obtained by the cetlciilation syst^.
Key Words: Computer, air conditioning, heating load, cooling load,
numerical method, room temperature, medium temperature, simulation,
radiation, meeisurement, intermittent operation, evetluation.
1. Introduction
The heating and cooling load of air conditioning is a heat that changes temperature and humidity
in the room being air-conditioned, other than produced by an air-conditioning syst^. It occurs in the
form of an external heat invading the room or an internal heat produced in the room. The heat from the
air-conditioner absorbs this heating and cooling load, thereby maintaining the temperature and htunidity
of the air in the room at a required level.
13ie calculation system that will be referred to in this paper is composed of the following two
principal parts:
1
Mechanical Ikigijieer
715
(l) Calculation of heat transfer and change in room air temperature relative to heat source equip-
ment output and heat medium transportation system.
(2) Calculation of change in the heating and cooling load in the room being air-conditioned.
This paper will deal with the subject, starting will the details of the calculation system. Then,
the result obtained from the calculation upon application to an existing building will be compared with
the actual measurement data to confirm the exactness of the calculation. First of all, the features of
the calculation system will be explained:
(1) The system gives a relation between cooling and heating load Q(^) and output of air-condition-
ing heat source Qjj3(^)t therewith enabling calculation of the room air temperature ^j(^) under an es-
tablished condition.
Despite the fact that air-conditioning systems are operated intermittently in many cases in Japan,
thermal changes at the early stage of operation and after the operation have not been much regarded. By
the said calculation system, such changes can be clairified.
(2) A relation between the time tj^ required for room air temperature d-. to reach a predetermined
level after the air-conditioning system starts operation and the capacity of the air-conditioning heat
source Qg^^j can be obtained, thereby permitting reasonable design of heat medium transportation systems,
(3) The calculation system deals with heat transfer by a numerical method. Cl»2) This elimi-
nates the need for any linearity or invariability of the thermal system and permits calculation inde-
pendent of such changes in heat flow and temperature. Also, the calculation system is easy for practiced
designers to understand, and caji be applied and improved without difficulty, thus offering wide use by
professional designers.
(k) In making up the calculation system, approximation methods of new concept have been intro-
duced; (a) Simulation of the heat medium transportation system in the air-conditioning system, (b) simu-
lation of radiant heat trainsportation in the room, and (c) simulation of heat exchanging in the air-
conditioning system.
The heating and cooling load in the room being air-conditioned is defined as a heat in a give-and-
take relation with the room air, where the heat causing the room air temperature to increase is expres-
sed as "positive" and that responsible for the decrease as "negative". Other definitions necessary in
the calciilation will be given as required.
2. Principal Equations Adopted in Calculation System
2.1 Ebccitations
Excitations are used as ain input factor to achieve the calculation, which can be obtained by means
of necessary relative formulae available from the design condition data. These formulae are prepared as
subrutine. While the design condition involves solar radiation, sky radiation, other effective radia-
tions, atmosphere, humanbody, animals, lights and heaters, their relation with the excitations directly
related thereto has been well known.
2.2 Numerical method of heat tremsfer
(1) Fundamentail equation of steady state heat transfer (2-dimensional)
K = . \ ...(1)'
d
where, Q. .: Rate of heat flow from point j to adjacent point i, d: Divided dimensions (see
figure 1), (^j^"'^.: Temperatures at points i and j. As Thermal conductivity. Assuming &2*"'
to be the temperatures at points 1, 2,... and to be the rate of a heat flow to point 1, we nave.
1
Figures in brackets indicate the literature reference at the end of this paper.
716
...(2)
For the steady-state heat transfer, the left member of the eq (2) is zero.
(2) Fundamental equation of unsteady state heat transfer (2-dimensional)
C = c.r.d^ ...(3)
a. At
P-— 5- ...(6)
d*^
d.o<
N = ...(7)
X
where 6-^ : Temperature at point 1 after time interval of dt, a: Thermal diffusivity, C: Heat
capacity of element volume, c: Specific heat, f: Specific weight. At: Time interval, o(: Heat
conductivity.
The various equations of heat transfer to be produced by the above fundamental equation and the
traditionsQ. equations will be illustrated in appendix.
(3) Temperature variation in thermal medium transportation system ( 5)
With a tube as shown in a figure 2 (1) considered to be a model of the thermal medium trainsporta-
tion tube, it is assumed that the surface of the tube is insulated, and the temperatures of the tube and
thermal medium are equal at auiy contacting point and time. Next, chainges in temperature with time at
respective points as shown in figure 2 (2) where the medium temperature is changed in step order as much
as aO"^ in the transportation system maintained at a constant temperature are replaced by lineair changes
as shown in figure 2 (3)1 and it is assumed that Q'^ changes at a uniform rate during the period of 2m1.<3t
to reach a final level, 0'^ corresponding to &^ that freely changes can be obtained by the following
equation.
2m1 2m1-m+1
'^2(n.dt) = '^I(n.4t-2m1./lt) ^ ^^1 f(n-2m1-«i-l) P "^^ sjet&n set up
by the conventional design method, thus given other results than those for rational equipment.
5.2 Comparison with measured values and evaluation
Changes of and 1$'^^ obtained from the actual air conditioning meEisurement in this building are
given in figure 8 (2) with dotted lines together with exterior conditions as figure 8 Changes of
heat medium temperatures are shown in figure 9 with dotted lines. The corresi)onding calculation results
are as given in figure 8 (2) and 9 with full lines and brocken line. A comparison between both results
snows that the change of Qijq, Q and 9^ with time shows similar vailues and trends. Although the heat
medium temperatures themselves are a little different because of difference in control method, the neces-
sary t^nperature difference are in near agreement.
What calls for specific attention here is the fact that the existing air-conditioning system is the
product of the conventional design method and not of a rational method. Also, when it comes to the
actual construction, there were unexpectedly many causes of heating £tnd cooling load, such as that from
the heat medium transportation system exposed on the roof. With these points taken into consideration,
a difference by 10% or so between the calculated and actual values for ^ggj is unavoidable.
For reference, the time and labor required for this calculation method are such that IBM 3^0 com-
puter took 20 to 130 seconds with 4t at 3OO to 60 seconds per one calculation day, and a little more
labor than for conventional method was required for input data preparation.
Judging from the above, we believe the practical value of this calculation method by degital com-
puter is very high.
6. Conclusions
In the future, calculations of the type mentioned above will have to depend on computers by all
means. As the calcxilation methods for solid heat transfer, there are weight function method, response
factor method and analog method, in addition to the numerical method employed in our system. All these
methods, however, pertain to the problem on less than 30% of the heating and cooling load, and ets to
remaining part of the load, they have little to differ. Uie gist of the heating and cooling load calcu-
lation should lie, not in the methodology of the solid heat transfer caJ-culation, but in the systenati-
zation of the calculation method altogether.
Our calculation method introduced in this paper has been systematized since several years ago, in-
dependently of the progress in other methods. With the numerical method, too, it is possible to reduce
the calculation time and memory capacity if proper consideration is given, and satisfactory results
724
could be obtfdjied in respect to acctiracy*
Improvement of this ceilculation method itself and interchange with other methods are the problems
ronaining to be solved.
This paper limited clarification to the design problems ahead of the heat source equipment output,
and has not dealt with the air conditioning energy. It, however, can be easily obtained using, the
handling of the heat medium transportation system as a guide, provided the performance of the system
components is already known.
While it is still premature to draw a conclusion because of insufficient data, the physical veilue
for the wall body, a ( = jjfy ) is considered different between cooling and heating period. For such
phenomenon, this calculation method is more advantageously applicable than other methods as in the case
of intermittent air conditioning operation.
To conclude this report, the author expresses his profound appreciation to Dr. Kenichi Hiraga under
whom he works for the opportunity of compiling this paper and very helpful advices and guidance.
7* Appendix
7*1 Various equations related to unsteady state heat transfer
Temperature in one dimensional object, see figure 11 (l)
^I.Zlt = ^^^^2 + <^3 + - 2)<^i) ...(26)
One dimensional, surface temperature of object in contact with fluid with temperatiire of, see
figure 11 (2)
•^l.^t " ^^^2 * ^'^t * - - ''^^1'' ...(27)
N. (9-x + 20-
or, = ^ — 1 ^ figure 11 (3) ...(28)
One dimensional, surface temperature of object subjected to heat flux q, see figure 11 Cf)
®l.At=2P(<^2*^i-''^^1 -^29)
Heat produced at uniform rate inside object Q, see figure 11 (5)
KAt = <^ - ^3 ^ - 2)ft, ^ Q ^) ...(30)
One dimensional, surface temperature of object with heat produced at uniform rate inside Q, see
figure 11 (6)
2
^^,it ' ^^^2 + N<^f + - N - 1X9-^ + Q|-j ...(31)
One dimensional, heat conduction between two objects, see figure 11 (7)
^1.At = ^(^2 - ^3 ^ - - -^^l)
^1 = -.^
1 1 ^2
725
where, Aj: Thermal conductivity of object with point 1, Ajj: Thermal conductivity of object
without point 1.
Two dimensional, irregular shape surface temperature of object
In case of figure 11 (8):
•^l.^t = 2P[^-^ + + N.^^ + - N - 2)6-^) ...(33)
In case of figure 11 (9):
^1.4t = *^3* 2 * ^'^f 5^ V '"^^^
In case of figure 11 (10):
^1.4t = ^^^-^ + N.^^ + (^ - N - D^J ...(35)
Value for K used in equations (33) to (55) is a corrected heat transfer coefficient inversely pro-
portionate to increase or decrease in area of the object surface.
7.2 Values of P and N
Because of the condition where multiplying coeffecient for in the right member of the equations
for &-)>At will not become minus, At has a permissible maximum limit. For example, tram equations (26)
and (27) given in the latter paragraphs, we have
P < 1/2 inside object ...(36)
P < 2('\^ti) object surface ...(37)
Also, the permissible range of P relative to any value of N is as follows: P £;l/3 ••.(38)
7,3 Surface heat transfer ( 3)
Q = a(& - (9-.) ...(39)
B 1
0( = C< +(X ...CtO)
c r
where, Q: Hate of heat transfer at surface, CX : Total heat transfer coefficient, 0^^: Convection
heat transfer coefficient, CXj.: Radiation heat transfer coefficient.
7.^ Badiation (solar) temperature O'g
& = ^ I + ...(41)
where, I: intensity of radiation, a: absorption rate.
7.5 Radiation ( 3)
%Z = *2^fl2S2 ^^105> - <10§> 3 •••<'*2)
726
Q-,2 - - S21 .^.ikk)
C .C
b
= ^2 ^ ^2 same wave length) ,..('f6)
where, Qi2^ ^^''^ rate of radiation from surface A-j to A2t A-j, A2: Areas of surfaces exchanging
heat by radiation opposite to each other, ^la* Total shape factor between A^ and Ag, T^, T2: Surface
temperatxires of A^ and A2, dA^, dA2: Small element areas in surfaces A^ and A2, <^^, f^' Angles be-
tween normals on oA^ and dA2 and line connecting dA^ and dA2, a^, a^' Absorption factors of A^ and A2»
e^, Snissitivities of A^ and A2.
7«6 Equivalent out door temperatiu-e &^ and equivalent temperatxire difference ( '*)
^e = ^sm*^C^,(T)-^em:i -^'^7)
4&e=<^sm*<'^s(t)-0-^i
where, Hoom air temperature, f: Decrement factor, T: Time lag, ^BiX)' Value of O'g as
much as before time being calculated*
8. References
( 1) H, S. Carelow and J. J. Jarger, Conduction ( 5) S. Kuramochi, An Calculation Method of
of heat in Solid, P.467~'t78. Air-Conditioning Heating and Cooling Load,
( 2) T. Kudo, Dennetsu Gairon, P.394~in6,
SHASHJ, Vol.43, No. 12, Vol.Vt, N0.I
( 6) S. Kuramochi, Investigation and Measxire-
( 3) K, Watanabe, others, Kenchiku Keikaku ments of Air-Conditioning on Buildings
Genron, P.29, 60. (I) (3), AHASBJ, Vol.44, No.2, N0.3.
( 4) H. Uchida, Kuuki Chyosei no Kihon
Keikaku, P.90 , 91
727
y
r
— d —
" T ■
1
~1
\ r-
L
1
1
1
-H ^
>2 ! 1
1 i
U -
i
1
_ J_
1
1
1
1
1
i_
i
1
1
1
1
. _J
-X
Fig-1 Heat Conduction in Solid, Two-Dimension
728
(D -X
Fig-2(1)~(3) Simulation of Thermal Medium Transportation
System
729
F fan
P pump
Pi control Panel.
P2 pump
Ti thermostat
Vi valve for heating
V3
V5 three way Valve
for cooling
Fig-3
A Model of Air-conditioning System
730
operation start
Fig-^- Change of Thermal Medium Temp. Just after
Operation Start
Fig-5 Change of Value of Qj^g, Q"pg and Q just after
Operation Stop
731
732
733
734
735
736
CIS
8 9 10 Uptime
Fig-lO Results of Calculation in case of enough Air
supply
737
(1)
Variation of Heat Transfer to be
738
739
f
(5)
Fig-U Cont. (4 and 5) Variation of Heat Transfer to be adopted
7A0
(7)
Fig-11 Cont. (6 and 7) Variation of Heat Transfer to be adopted
741
742
743
Heating and
by Means of
Cooling Load Calculations
Periodic Window Function
Kazuo Eguchi
Building Research Institute
Ministry of Construction,
Japanese Government
One of the computer calculation procedures for the determination of heating and cooling loads, is
presented in this paper. This method uses time series on assumption of linearity and s ta tioneri ty . The
concept of "window function" is introduced as combining function of time and time-series. The "triangu-
lar wave function" is considered as one of the periodic window functions that are practically easy to
handle. The problem of heating and cooling load on building is assumed to be a periodic phenomenon, and
this justifies the use of periodic window function.
The calculation procedure is first to determine the "heat flow matrix", of which elements consist
of rate of heat flow emanated from each room for a given time, and this rate of heat flow assumed to be
proportional to the room temperature. In the case of intermittent heating and cooling, the room temper-
ature and rate of heat supply are alternately unknown. Then, both unknown temperature and heat supply
rate is collected, and heat flow matrix is transformed into "thermal matrix". To determine the thermal
matrix is to obtain the heating and cooling load and the fluctuation of temperature in each room at each
time. In its principle, this method is readily understood and computer programing is also easy. In
addition multi-room problem and completed time schedule of the indoor design condition can be easily
handled.
Included in this report are an example of heating load evaluations for dwelling with five rooms and
for building of which the whole space above the ceiling consists of a plenum chamber.
Keywords: Heating and cooling load calculation, window function, time-series, triangular wave
function, response factor method, heat flow matrix, thermal matrix, warming-up period, duct-type
room, multiple rooms. Gauss elimination, Gauss-Seidel method.
1. Introduction
Recently computer has come to be widely used in the field of architectural engineering. With res-
pect to the calculation of thermal load of buildings, for example, ASHRAE's Task Group on Energy Require-
ments has developed a calculation procedure [l] based on the Response Factor Method [2], [3] •
From the stand point of engineering usage, load calculation using computer will have to take account
of the following points.
(1) Accuracy from engineering point of view.
(2) Applicability of commonly used computers.
0) Short computation time.
(4) Simplicity in the preparation of input data and in the operation of partial modification of the
data.
(5) Wide range of application.
Research Officer, Building Physics Section, B.R.I,
figures in brackets indicates the literature references at the end of paper.
745
It would be difficult .to satisfy all these points. It is therefore desirable to prepare several cal-
culation procedures having their respective characteristics features, so that designer may be able to
choose a most efficient procedure according to his objective.
In this paper, a calculation procedure for periodical heat flow problem is prevented. The method
of solution is based on the principle of superposition, which assumes linearity and stationerity .
2.1 Time-Series and Window-Function
"A time-series is just a series of numbers or quantities representing the values of a function at
successive equal intervals of time." [3]
The time-series is assumed to be an approximation, using a finite number of information, of a time-
fumction which varies with time. Thus, a concept of "window function" is introduced to relates arbitrary
time-function to its time-series.
There are two types window function wf(t), i.e. transient type and periodic type which have the
following properties
wf(0) = l
Transient type J wf(N./)= 0 ;N±{1,2, ) (1)
[ (t)dt = J
Periodic type Jwf (t)= wf(tf;j.T) ;N±(1,2, )
wf (0)= 1
wf(N"Zl)=0 ; N'=l,2, , T/A-1 (2)
jjf(t)dt = zl
where J is the time interval of time-series and T is the period.
If a time-function f(t) represents a periodic phenomenon, it is convenient to use a window function
of periodic type, and if f(t) represents a transient phenomenon it is necessary to use a window function
of transient type.
If F(N) ; N=0,l,2, is the time-series of f(t), then the approximate time-function f ' (t)
represented by this time-series is given by the following equation,
f(t)=lF(N).wf(t-N.J) (3)
where Z stands for 21 J.f wf (t) is transient type and forjr if it is periodic type. The terra of the time-
series is a time-function obtained by the product of the window function having time origin at that point
and the value of the time-series.
From eq(3)
f (N.Zl)= f (N'J) ; N=0,l,2,
f(t)^f(t) ; t=N-J
746
In general, f'(t) is identically equal to f(t) in the limit as time interval /I approaches infinitely
aoall. IfJis a finite time interval, f'(t) is an approximation to f(t) at • 3) .
If J has a fixed finite value, the degree of approximation depends on the property of the window
function as well as that of f(t).
In response factor method [l] , [2] , [31 , the triangular pulse is used for window function.
There exists infinitely many window function satisfying eq(l) or eq(2). However, it is desirable
to choose one on practical consideration such as precision and ease of handling depending on the case.
Figure 1 illustrates some examples of window function of transient type and periodic type.
2,2 Triangular Wave Function
Triangular wave function is a window function of periodic type which is represented in the form of
Fourier series. Such functions are infinite in number, and the following is a relatively simple one
r (mnN/2)-1 ( f^-] 1
twfrM(+)-('/^'^ l+-C2/M)-EC0S(J-x) l+Z(2i/M)-C0S(J-^-(M-i))
J = l i=i ■'
+ (Ml)-C0S(M-NN-X/2) 1 (5)
where X =(2TT/T)-t
NN =T/A (even number)
M =1 ,2, — (in the following, M is referred as "order")
C ^ = 0 ; M = even
[0 ^]/^ ; M = odd
The degree of eq(5) as a polynomial in trigonometric function is (M«NN/2). The lowest degree
of the triangular wave function is NN/2, which corresponds only to eq(5) with M=l, that is.
Ml , > (NN/2 ^
iwV^u^v =[1/NN)- ly-cos(j-x)
lj=0 J
(6)
where if = 1 ; J = 0 and J =lMKl/2
J =2 ; J = 1.2,-'--,NN/2-l
Substitution of the windo-v function twfjj^ of eq(6) in eq(3) gives
= Yfm-tvj\^^{t-u-A) (7)
■X)j (8)
or HN/2 ,
f'(t) =Z 8- a(K>COS(K-X)+b(K)-SlN(K
K=0 I
where nn
a(K) = (t/NN)-Z FCL)-COS(K-L-J)
u-1
b(W=(l/NN)-Z: F(L) ■SIN(K-L-J)
747
Equation (8) represents the result of harmonic analysis of NN time-series, and is the lowest degree
Fourier series pa^ssing through NN points. Expressions in eq(8) are called Fourier coefficients. Hence,
when we use twffjfjfor window function, representation of periodic function f (t) by the time-series F(N)
and representation by Fourier coefficients a (k), b(|<) (k= 1,2, , NN/2) are identical. Method of
analysis using Fourier coefficients a(|<), b(|^) or using amplitude and phase constant obtained from them
is called the frequency response method. Characteristic feature of the Jjroblem of heating and cooling
load calculation which is different from the general engineering problem is that i) in the ordinary
intermittent heating and cooling, the unknown time period for temperature and heat flow rate appear
alternatingly, and ii) that the problem is not determination of response to a particular frequency but
determination of the resultant temperatures and heating loads superposed over the whole frequency range.
In this respect, the method of time-series which can treat the temperature and thermal load at each time
period directly as unknown variable is more convenient that the frequency response method.
Oi the other hand, as for approximation of uniformly continuous curve, use of twf^' for window
function is generally better than the broken line approximation (use of triangular pulse for window
function) or the step function approximation (use of rectangular pulse for window function). However,
in the thermal problem of buildings where discontinuity points appear in cases of beginning and termina-
tion of heating and cooling or on and off of illumination, approximation using the window function twfNW
is not sufficiently good because of the appearance of overshoot immediately before and after the time
period. Equation (5) is made up, considering these points and the overshoots are reduced by increasing
the order M. The relation between M and overshoot is shown in (fig, 2), where M values in even number
are superior to those in odd numbers. With the order M gradually increased, eq(5) approaches a periodical
Triangular pulse.
2.3 Response of Sjstem Elements
Thermal system of a building or a room is the set of basic elementary system such as heat conduction
system of wall and floor and heat transfer system of ventilation. It is therefore required to determine
the response of these basic system elements in the first place. The response time-series of the system
corresponding to the window function input is denoted to be R(N).
The output time-series G(N) of the system corresponding to the input time-series F(N) is given by
G(N)=ZF(M),R(N-M) (9)
where I stands for^2.^if the window f'onction is transient type and f or E if it is periodic type. Thermal
response of wall and floor corresponding to artificial function such as triangular pulse and rectangular
pulse is generally an infinite exponential function. Thus in practical computation, it is necessary to
produce approximation by cut-off or rounding, and the error produced by such approximation will be
referred to as "internal error" in this paper. In contrast with this, approximation error in representing
a time-function by time-series as previously described and the hypothertical error regarding input will
be referrd to as "external error". When artificial function is applied to window function, the final
estimation of errors are very difficult, as both of the internal and external errors are included in the
result of calculations. While, the thermal response of walls and floors corresponding to the trian.gular
wave function expressed by Fourier series being easily and accurately calciilated, therefore, only external
errors are considered.
3. Construction of Calculation F^cedure
3,1 Heat Balance Equation of Room Air
and Heat Flow Matrix
The following description in this paper adopts an approximation neglecting the energy interchange
by radiation from enclosing wall surfaces. In other words, it is aussumed that the heat transfer between
the surface of waJJLs and floors and air is propotional to overall surface conductance and that overall
surface conductance is invariant with respect to time. The problem is dealt with the multi-rooms problem
and totaline; number of the rooms is denoted by JJ, Heat flow matrix denoted by[THlis a matrix whose
element in row (^) and column {j^) is the coefficient of the rate of heat flow flowing out of room J at
time M.*z) with respect to the room temperature T(n ) of room I at time N*zl. Heat flow matrix is a square
matrix whose dimension is given by the following equation
NXJ=JJ.NN (10)
748
where
NN= T/4
T = period
J and 1= Integer denoting room number
M and N= Integer denoting time ( in the later description, U.A and N.J .
are replaced by M and N respectively for simplification)
Heating or cooling load H (J,) and the room temperature 'V(li) are presented in the column matrix (Hj
and [TJ respectively. Heat supply into room air caused by atmospheric temperature, solar radiation,
illumination and heat generation of the rcom occupants, which can be calculated independently of room
temperature T(5) and thermal load H(m), is denoted HO(S), of which column matrix is symbolized [H|.
Now, heat balance of room air is expressed in matrix form as
(TH). [T]l-[Hj=tHO]l (11)
Heat flow matrix [TH] represents the characteristics of thermal response of building with room
temperature as input and heat quantity as output, if interchange of air by ventilation between the ad-
joining rooms, the heat flow matrix is a symmetric matrix. The inverse matrix tTH)"^ of heat flow matrix
[TH] will be named temperature matrix and shown as [HT) . The temperature matrix IHTI represents the
characteristics of thermal response of building with heat quantity as input and room temperature as
output.
3.2 Elements of Heat Flow Matrix
The element of heat flow matrix TH(M'N)is given by
TH = -W1+ WO-?I+VO+HFA+HAA (12 )
The terms are defined as follows.
1) Heat gain by conduction from walls and floors (WI),
Wl(^'L)i^j =2WS(I,J,K)-Y(K,M-N) (13)
2) Heat loss by conduction into walls and floors (WO).
WO(S';^)i=j=?ZwS(l,J,K)-X orZ(K,M-N) (14)
1=1 K
where
WS(I,J,K)= area of wall No. K, that facing to both room I and J,
JT= J J -I- numbers of atmospheric temperatures (room temperatures known
at each time are considered as atmospheric temperature).
X(K,M) ]
Y(K,M) = response time-series value of wall No.K at time M.
Z(K,M)
Representation of X, Y,Z,are in accoi and using these quantities, thermal loads can be obtained
by simple multiplications and additions. In case the dimension of the simultaneous equations (NXJ-W)
is not too large, they can be accurately calculated by well known "Gaussian elimination".
In Case the dimension is large, the "method of succesive displacement" (Gauss-Seidel method) is appropri-
ate. In case of applying the method of succesive displacement, unknown variables are successively
determined along the time elapsing, calculating the small matrix of dimension equal to the number JJ
at each time. (cf. table 16)
751
During the warniing-up period, the small matrix expanded up to the terminating time of warming-up
period (dimension of matrix is an integer multiples of JJ). (cf. table 17) In case duct type room is
care must be taken in calculation, as principal diagonal of the matrix sometimes contains ^ero.
In addition, response factor method can be considered to solve a matrix of infinite dimension by successive
displacement. That is, since the transient response to the pulse input of wall and floor becomes almost
zero, after a long time, calculation steps of the successive displacement method after this time period
yield almost exact solution successively, if we proceed by arbitrarily setting up an initial condition.
Generally speaking, decision as to the choice between Gauss elimination and successive displacement
method depends on the capacity of the computer and the dimension of the matrix to be solved.
k. Example Problem
Two examples are shown in the following.
Both have their principal objective to seek the peak load and the daily total heating load when the
designeted time schedules of intermittent heating are changed. Periodic triangular pulse is used for win-
dow function and calculated with^=l hour and period=24 hour. Solar radiation, mutual radiation change
between surfaces and heat storage of furnitures in room are neglected. Latent heat load is not included.
Thermal matrix [^] was solved by Gauss elimination and the computer used was TOSBAC- (core memory
16 m, magnetic disc KW)
4.1 Example Problem (I),
Heating Load of Dwelling
Heating load for a dwelling unit of an apartment house as shown in (fig, 3) is calculated.
Adjacent units up, down, right and left of the unit were assumed to be in the same thermal condition as
the objective unit. The dwelling was divided into four rooms and one stair room (commonly used by
dwellers in other houses). Arrangement of walls and floors, their composition and area, thermal constant
of materials and air volume of the rooms are respectively shown (fig, 4) table 4, 5, 6. Assuming the
life pattern of four family members as shown in (fig. 5), the heat quantities to be generated by lighting,
electric appliance, cooking and human bodies roughly estimated by the said assumption are shown in table
7 (cooking heat is over estimated). The natural ventilation between rooms is classified by night time
and day time and shown in (fig. 6), Assumption on five patterns concerning design temperatures in each
room and their time schedule is shown in table 8. Designed outside air temperature adopted for calcula-
tion is shown in (fig. 7).
Plesults of calculation concerning the heating patterns A, B, C,D and E are respectively shown in (fig.
7-11). Total sum of the heating load for rooms [I] - [4] at each time is shown in (fig, 12) by heating
patterns. The relation between peak load and daily totil heating load is shown in table 9« Results of
calculation indicates the big differences between heating patterns.
Since the temperature environment in room itself varies with the heating pattern, comparison by
peak load and daily total load alone is difficult, Ptoughly speaking, however, programmed control (E
type) is considered to be superior.
4.2 Example Problem (II),
Office Building with Duct Type Room
Heating load and fluctuation of room temperature of an intermediate story in an office building with
center core as shown in (fig. 13) are to be calculated. Upper and lower storey of this storey are assumed
to be in the same thermal conditions as this storey. Heats generated from human bodies and lighting
devices are neglected. Various values for calculation such as composition and area of walls and floors,
thermal constant of materials, and air volume of rooms are^ respectively shown in table 10,11 and 12.
Two kinds of warming-up period (2 hours and 3 hours) for calculation are shown in table 13, Three kinds J
of assumed ventilating patterns A,B and C are shown in table 14. Explanation of RHS patterns 0, 1, 3 '
for calculation is shown in table. 15,
752
Here RHS is the ratio of "ratio of heat supply to duct type room" and "sum of heat supply ratio to
duct type room and to main room" during warming-up and specified temperature period in main room.
Combination of warming-up period, ventilation pattern and RHS pattern for calculation is represented as
shown in the following example.
( 1 , A , 1 )
I T ^ . n
warming-up period ventilation pattern FHS pattern
Calculations are conducted for nine combinations such as (1, A, 0), (1, A, 1), (1, B, 0), (1, B, 1),
(2, A, 0), (2, A, 1), (2, B, 0), (2, B, 1), (2, C, 3). Result of calculation are shown in (fig. lA-22).
The relation between peek load and daily total load of each calculation are shown in (fig. 23).
Although this is only one example of calculation, referring to the results of such caluculation,
designers may be able to choose the rational and economic equipment and air conditioning system of
building.
5. Conclusion
Solution by means of time-series is cleared by the concept of "window function". Window function
can be chosen at liberty according to the problem, and when treating periodically fluctuating phenomenon
use of "triangular wave function" is appropriate. In the problem to predict room temperature fluctuation
and thermal load of a building, "heat flow matrix " plays a fundamental role. Unknown quantities such
as room temperature and thermal load can be determined by solving "thermal matrix" which is obtained by
a transformation of the heat flow matrix on the basis of indoor design condition (time schedules of inter-
mittent heating or cooling and existence of duct type room) and outside condition (solar radiation,
atmospheric temperature etc.), TWo method for solving thermal matrix, i.e. Gauss elimination and method
of succesive displacement are selectively applied in compliance with the nature of problems and the
capacity of computer to be applied.
With the method of calculation described in this paper adopted, the problem of intermittent heating
of multipls rooms can be treated as ordinaly one and the problem for single room only becomes rather
special one. The periodical phenomenon is treated in the present paper, however, by extending the
period T to infinity, the response factor method may also be considered to be included in the calculation
method described here.
The effects in case time schedules of intermittent heating are changed, are mainly explained in the
said examples of calculation. Ease of such calculation will be a great help to the designers and will
facilitate them in their more accurate overall decision making.
6. Fteferences
1 Proposed procedure for determining heating 3
and cooling load for energy calculations,
The task group on energy requirements for
heating and cooling, ASHRAE. ,.
D.G. Stephenson, and G.P. Mitalas, Cooling load
calculations by thermal response factor method,
trans. ASHRA3., vol.73, part I, ,
2 G. P. Mitalas, and D. G. Stephenson, Room
thermal response factors, trans. ASHRA3., vol.
73, part I, I967.
4 K. Eguchi, A method of space temperature and
and heating and cooling load calculations by
window function and time series, trans. AIJ.
Summaries of Tech. Papers of AIJ. , AUG. .
753
7.
Appendix
Solution of Thermal Matrix by
Method of Successive Displacement
(1) The case in which all unknown variables are room temperature (problem of room temperature fluctua-
tion)
(2) In case room temperature is specified (without warming-up period)
As shown in table 2, dimension of the simultaneous equations to be solved at that time decrease
comparing with the case of 7X1) (cf. table 16), however, the method is basically the same as above
(cf. table 2, 3, table 17).
(3) In case warming-up period is provided
In a simple example shown in the table 17, small matrix expanded until the time when warming-
up is finished must be solved, (cf. table 17)
Considering the case when warming-up periods in different rooms and specified temperature period
are overlapped, the said expression must be corrected as follows for making the expression more
strict, i.e. "snail matrix expanded from the time when v*araiing-up period is started in any room
to the time when warming-up periods are finished in all rooms". However, same as the case shown
in table 3, dimension of the simultaneous equation decrease less than appearance.
754
Function of iime by time-sen'es
(A ) Transient typed window -function and windoi^/ -function
Notes : T ; Periodic time , A ; Time sejment of time-series.
Fig. 1, Example of window function and function of time as represented through superposition
of the former.
755
Fig. 2, Example of trianguler wave function (twf kjij ) and relation between its order (m) and
overshoot.
Plan @
Room No.
Descn pt .on
m
Living rm. (a), Bedrm.Cb), Kitchen Cc)
Bed rm. and study rm.4or chi Id ( I )
Bed rm. and study rm. -for child ( E )
s
Entrance hall, bath rm., lavatory ^
Stair-case Ccommon use )
@
Out side air ("South Side) 1 ^
0
ditto (North Side) i
^ ; PoomCa),(b)andCc')ar€ gathered and computed as room IT] .
*»; AsSumif^g that: temperature of B is ecj^ual to that ot [zl ■
Fig. 3, Example problem (l), Heating load of dwelling. Sketch of dwelling used for calculation.
756
. 12 13 12 13 12 13
0
0
f7)
(8)
N5Z2ZZZ7
5
5
5 5
4 S
1
( 13
(6)
(3
J,
H]
(■9)
E
(7)
0
(8)
(7)
:$4
13
13
13
0
Notes j Figures in D show each room Mo..
Fiaures in ( ) show No. of each floor. ) ,
^ K'SeeTable4 3
Others show No. of each wall
Fig-. 4, Example problem (l). Heating load of dwelling. Arrangement of wall and floor.
757
Hour 0
12
15
18
21
24
Husband
□
m
E
m
(b)
(b)
Wife
m
m
|l.2,3,4|
m m
m , m
m
(b)
(C )
Child (I)
m
m
□ H
H
ta)
fa:) T-"^^
Child (I)
(D
CD
m @
Note : Dotted lines indicate sleeping hour and figures in D indicate
the number of room.
Fig. 5. Example problem (l), Heating load of dwelling. Assumed living pattern of an occupant.
(Number of family members : 4)
Night ti
me
Time (l7, 18, ,24, 1 ,- - 8)
84
42 48
o'clock
63 51
Daytime
Time ( 5. 10, -•- , 16)
f68
150
El
, . , „ .30
m
(44
48
16
Fig. 6, Example problem (l). Heating load of dwelling. Natural ventilation betvreen rooms.
758
II 234 I Tetnp.
20
01
Q_
e
0)
10
Remarks:
Real- line ; Room air temperd"ture
BroKen- line; Heating toad
Figures in □ indicate the No. of room.
>! X — < X — ><■ — X — -V
[UTemp. /
y. — ■>< — y — y — X — X — X — >
Outside air temperature
1 d / g] \ T / T>
\ if
o
A
«3
U
o
CO
c
t^
X
1/
0
12
(6
24 hour
Fig. 7, Example problem (l), Heating load of dwelling. ( Heating pattern A )
759
20
u
o
\ I
<— X'— X— X —K
Temp.
Temp.
( the same remat-Ks
as that of F;g.7 )
-43
A -A
12
18
5
O
24 Hour
Fig. 11, Example problem (l), Heating load of dwelling. ( Heating pattern E )
763
764
Plan
(6)
(5).
(6)'
(2)/3)
(7),(8)'
of centei--core
Section 'I j
HI '■ Office roomCMam room)
[2] ; Space over cdling ( Duci-type room)
[E : Corridor and center- Core
SJ: Ouiside air
Mote: Figures in ( ) desijnd"te the number of I
and -floor indicating fhe'ir COnnposit ion .
( See Table 10 ) .
Pig. 13, Example problem (ll). Office building with duct-type room.
Sketch of office building used for calculation.
765
30
u
Warming up
Ventilation
patte
2 hour
rn •. A
: 0 (non- duct- type room^
10
/
Out Side air temperature
200'
xio'
(supplied to H]
o
o
-© — e — e — e — e — i — e-
o o o — o o o 6
0
12
hour 24
Fig. 14, Example problem (ll). Office building with duct-type room.
Combination of design condition : ( 2,A,0 )
766
767
Warminn up : 2 hour
^ I
Ventilation pattern '. B
RHS pattern : 0 (non- duct-type room)
200
X10'
. Heating load (supplied to 0 )
V
\
100
13
o
-o — e — e — e — e-
12
18
hour
24
Fig. 16, Example problem (ll), Office building with duct-type room.
Combination of design condition : ( 2,B,0 )
768
30
IVarmln^ up '. 2 hour
Ventilation pattern '• B
Fig. 17, Example problem (ll), Office building with duct-type room.
Combination of design condition : ( 2,B,1 )
769
30
Warming up : 3
Ventilation pattern
RHS pattern : 0
hour
: A
C non-duct-type room)
200
x10"
Heatinj load (supplied to 0
100
KJ
o
-4-)
6— o — Q— G — e — e-
C,3 )
774
RemirKs
Warming up
hou r
No. of RHS
pattern
OdAl)
•(?• ( 1 B 1)
(lAO)
•
@ (2A 1 )
0
1
|h
•
o
®
©
show the vent; lation
pattern B
(IBO) •••
(2B0)-®
•6-(2BI)
®
(2A0)
(g) (2C3)
q 10 11 12
Dally -total load [Kcal • day"' ]
Fig.23> Example problem (ll), Office building with duct-type room.
Peak load and daily total load.
775
Table 1. An example of heat flow matrix [TH]
~T;me
-Room NN = 4
J J = 2
MX J = 6
t ^Room
Time
Symbols used +o show the composifion of ma+riX element
A/alland Floor
Ven+ilation
Furnitui-e
Room air
Desctlp^:ion
Symbol
WI
WO
VI
VO
HFA
HAA
Derailed term ofrnotrix element
I = J
N=M
•
•
•
•
A matrix element sho*/n in the
symbol column left side
l-epresents summation morked
terms on the righthand.
N¥ M
0
o
O
O
N = M
m
•
•
B
O
Notes
• : Vdlue of response to window -function input when time is zero.
o: Values of response tro window function input when time is not zero.
IN
1
2
3
4
M
\ I
J\
A
B
A
B
A
B
A
B
A
X
/
/
/
1
B
X
/
/
—
2
A
/
X
/
/
/
—
B
/
X
/
3
A
/
m
B
/
X
/
4
A
/
/
B
/
W/
Table 2. Thermal matrix [""iV] in which warming-up period is not included.
Time schedule
Period of desi^riated
temperature (|S5
Room A
time 2,3
Poom B
3,4
unKnown ->-
-
- T -
- >
-- H -
1
2
3
4
1
2
4
2
3
3
4
A
B
A
B
A
B
A
B
B
B
A
A
A
B
B
1
A
0
0
0
0
1
A
m
/
1
B
0
0
0
0
)
B
y
i
/
2
A
1
0
0
0
Exchange
of rows
2
B
u
2
B
0
0
0
0
4
/
3
A
0
1
0
0
2
A
/
X
X
1
3
B
0
0
1
0
and of
Columns
3
A
/
X
1
4
A
0
0
0
0
3
B
/
0
1
4
B
0
0
0
1
4
B
X
X
I
-Time
Room
(Empty space is 5ame aslTH] matrix element )
/ Por"l:ion enclosed with bold line is
coefficient matrix of simultaneous linear
\ e^j^ua-tion to solved.
776
Table 3- Thermal matrix [TV] in which warming-up period is included.
Time Schedule
Warming up U)
Des:3nal:ed('/3)
Room A
Time 1
2, 3
Room B
2
4
.
Room 111 is kept at I7°C continuously.
2
j 20
7-21
3
4-
1 7
24
D
1
23
7-2 1
Room D] is same as above.
Room IHand IE are heated at 20°C
only when children use them.
Room [4] Is not heated.
2
1 20
14-2!
3
4
not heated
E
1
[ 23
7-21 ]
Aufomatic -temperalrure conhrol for
varying temperatures in different
time zones is assumed.
2
U 1 8
Other hours '
3
r 20
7-21 )
1 18
Other hours J
4
1 7
0-24
No-te ; Room H] is not hea-ted any heatin^^ pa-tterns.
Table 9. Ezample problem (l), Heating load of dwelling. Peak load and daily total load in
each heating pattern.
Heating
pattern
PeaK load
CKcal - h-' ^
Daily total toad
[Kcal-day"']^ 10^
4 100
6 590
5 510
5 560
4 600
83.5
77.8
71. 5
61.7
72.2
781
Table 10. Example problem (ll), Office building with duct-type room.
Composition and area of walls and floors.
Mo.
Building
elemeirt
LompoSiXion or
ma'beriSil and
'liiS Idyered
IS)
iD
C
:^
ct
^
h-
[m.ml
Heat tranSTer
out: 11 1 L t c_ r 1 0
LKcal.n .m c j
Facing rooms
Area
[ m ^ )
1
Cei ling
Airfiibove surface)
8
m-[2]
28 5 5
Rock wool
18
Air (under 5ur-face )
8
2
Floor
Air ( above surface )
8
(048
4T4
L',_ght-wei5h-t- Concrefe
155
AirCunder surface)
8
3
Floor
ditto (except ffiicKness of Light- wei^ght
concrete 80 )
180 7
8 1 G
4
Door
Air (5urf ace )
6
29
Steel plafe
(nej 1 Ig 1 ble )
Air space
10
Steel plate
(negligible)
Ai r ( Surface )
G
6
Window
Airfoatside surface)
15
3 2 0
Glass
( n 65 1 i q i b 1 e )
Air Cinside surface )
G
6
wall
Airfoutside surface)
1 5
3 24
34 0
Metal sKm
(negligible)
Air space
1 5
1 nsu 1 atlon
30
Air space
10
In su lation
30
Ply - wood
5
Airfinside 5urface )
6
7
Pariihon
Air (^urface^
403
Plaster
15
Air space
5
Plaster
15
A i r C6urf ace )
G
8
Pdr-ti-t-.on
Air (surface )
G
[0-0
1 3 5
Li^ht- weight -concrete
120
Air (surface)
G
782
Table 11. Example problem (ll), Office building with duct-type room.
Thermal constant of materials.
Md-terial
Thermal conductivity
[Kcal-h-'- m-'.^C-' ]
Thermal di-ff usivity
[m2-h-' ) * 10"^
Rock wool
O.O 64
4.9
Ligh-t - weight
conchete
0.5 8
14. 0
Insu 1 1 o n
0.1 3
11.3
Ply - wood
0. 1
3.6
Plaster
Q. 5 5
2.0
Table 12. Example problem (ll). Office building with duct-type room.
Air volume of each room.
Room Mo.
Room
Air volume Cm
m
0"ffice room
Space a^bove
eel 1 i ng
Corridor and
center- core
783
Table 13. Example problem (ll), Office building with duct-type room.
Daily heating pattern ( Designated temperature and its time
schedule ) .
Room LU
Period of non- designated "tern pera-ture
f Temperafure change)
?er\oi of Wdrming-up
(Constant load)
feriod of designated
temperatuf-edoid change)
2 hour
warming-up
Time 18, 11 — ,0,1,- ,6, 7
8
1 9, 10, ---JV
Pesignated temperature is 20 *c
3 hour
wdrming-up
I8jq,- - ,0, 1. ,6
■7, 8
If should be noted that the term warming-up hour is meant as 3uch
sinown in the following charts, on account of the periodical triangular
pulse bein^ used as window function.
Hedtinj load
2 hour Wdrming up
Heatirig load
3 hour warming up
T 8 9 Time
€.769
d) Deiigndted
j temperature
period
* Ti me
Room [2j dnd [1] are conf;'i nuously non - designated temperature.
Table 14. Example problem (ll), Office building with duct-type room.
Daily pattern of ventilation between room.
Symbol of ventilation
pattern
Period of non- designated
temperafiure
period of
Warmi ng-up
period of desijna-fced
tern peratrure
A
o/
r
B
o(
C
1 m
m
IU^
1'
1 f—^
^ '
[ ^
E _|
Nion- venti lated
Only 5lr circiila-tion
between D] and S
(without -flesh air supply)
Unit :Cm^h-']
784
Table 15. Example problem (ll), Office building with duct-type room.
Daily pattern of RHS.
_ Ratio of heat supply to room \z\ (Duct- iype rmQ
Ratio cf heat supply (to room [1] + to room iT]( Ma m rm.))
No. of RHS
pattern
Descri pfion
0
Necessai-y heat dmount is directly supplied to CD (fnain rm. ).
f There's not duct-type room)
015 main room and [2 is duct- type room.
Necessary heat is directly supplied to [1] (duct-type rm-^
E i5 main room and H] is duct-type room.
Necessary heat is directly supplied to Hi during warmlnj-up p€r,od of |j]
During the designated temperature period of [D , the necessary hea.t is
supplied to both U] and \2i according to following assumed
R 1-1 S values m var
hour.5.
Time
q
1 0
1 1
12
13 - 17
RHS
0.1
0.2
0.4
0.8
1.0
785
Table 16. A case where all unknown is room temperature.
A B
4
ABA
-Time
- Room
Table 17- A case where warming-up period is included.
Time 5chedu le
T; me
1
2
3
4
A rm.
Men- designated
VVdrrnin_g - up Coi)
desig nated C/B )
C
B rm.
Nion- desijneted
\
N
1
2
3
4
*-Ti me
M
H
A
B
A
B
A
B
A
B
- - Room
1
A
W/
X
t
\
-(u
nl^nown iS hea-ting load )
B
W/
m
2
A
W)
i
X
1
0
B
X
1
0
0
3
A
X
1
X
B
X
0
1
4
A
fa)
\
X
< — (A case of Appendix
B
0
786
BANQUET ADDRESS
Computers and the Building Industry
S . Daryanani
Syska and Hennessy, Inc.
Computer technology has made amazing advances within a short period of the last two decades. The
computers are being utilized in many phases of business and industry--from guidance of missiles to op-
eration of meat packing plants for optimization of meat mix for hot dogs. Considering the popular ac-
ceptance of the computer in today's technological society, one would expect to find extensive utiliza-
tion of the computer throughout the building industry. Surprisingly, the degree to which computers
are actually used in the building industry is very slight. Even the design disciplines do not make any
significant use of it.
Compared to other industries, the building industry is just starting to utilize the computers.
Several engineers have developed impressive problem-solving programs. Most of you are already familiar
with programs developed by APEC. Some large-scale computer systems have been developed and implemented
for structural analysis and construction project management. However, all the computer utilization at
the moment does not replace even 5 percent of the total design manpower involved in the building indus-
try, and therefore is insignificant and somewhat discouraging.
Why the building industry is not using computers at the moment
There are several reasons for lack of utilization of computers in the building industry.
We are proud of our building industry here. People all over the world are fascinated by our high-
rise buildings which are ever leaping skyward. Visitors are always anxious to see the latest projects
of our architects and engineers.
While we are proud, we should also be realistic.
If the building industry is compared with any other automated industry, such as the manufacture of
automobiles or television, the problems will be evident. The construction industry has scarcely reached
the level of mass production. Strangled by lack of organized research, outdated building codes and con-
servative trade unions, it has remained, in a large measure, a pre-industrialized craft. The industry's
rate of technological advance is far below that of other industries. We know the more advanced the
technology, the easier it is to automate.
The building Industry is large but consists of several forces pulling in different directions and
therefore lacks a sense of direction. The professional talents required in financing, design and con-
struction of a large building are amazingly diverse. For the sake of explanation, these can be clas-
sified into one of four general sectors: Management, Design, Construction and finally. Operation and
Maintenance.
Let us consider the problems associated with the design disciplines, though extensive computer
usage could also be made in the other three sectors.
787
The Architect has been the leader of the design team — and safeguards the owner's interests during
design and construction. Due to the widely divergent and highly technical nature of many aspects of
building design, the architect has to depend on professional consultants in the engineering areas, such
as the structural engineer, the foundation engineer, the mechanical engineer, the electrical engineer.
The design team may also have the cost estimator, the interior designer and the specialists in acous-
tics, illumination and landscaping.
This diversity of intellectual disciplines involved in the building design generally fragments
the building team in several ways, the most important being the intellectual fragmentation. The archi-
tect does not appreciate the mechanical engineer's goal. The mechanical engineer does not care about
the electrical engineer's objectives; and so on. The design profession is like a universe with several
planets, each merrily surviving in its own orbit.
The most damaging consequence of this fragmentation is the problem of communication. As we know,
communication is the binding force of any social unit, be it design or construction of buildings.
Various disciplines cannot be integrated without communication and professional interaction.
The lack of communication always results in suboptimization of design. Conceived without communi-
cation, the best structural design can force a suboptimal mechanical design. A solution based on
initial cost may be viable on the basis of the operating cost. The optimized building design is more
a matter of communication than of linear programming.
The last consequence of lack of communication is expensive duplication of effort. The same infor-
mation is handled over and over again by different persons involved in the process of design.
Another reason for lack of use of computers in the building industry is due to the rais-match in the
requirement of the building industry and the present applications of the computer. While the major prob-
lem in the building industry, in design and construction, is that of communication, the present computer
applications are geared mainly to engineering problem solving. In addition to problem solving, what we
need is a system which will consolidate all the information about the project in a central file of data
where it will be available to all the members of the design team at the same time. The availability of
data to all designers will allow for analyzing the impact of design decisions made in one design area on
the other aspects of the overall design. Thus, engineers could develop integrated designs in terms of
overall project goals instead of being limited to their own discipline.
Most of the computer efforts in engineering to date have been aimed at problem solving capabilities.
As you know, the major effort of engineering is not problem solving but integration of the solutions to
form a project. Therefore, concentration on the problem solving capabilities has fragmented the work
that can be done on a project with the computer, and has slowed down application of computers to solu-
tion of communication problems.
The problem solving approach to engineering has resulted in two handicaps which have again affected
utilization of the computer.
First of all, there is duplication of effort since each problem solving program contains repititions
or large parts of some other programs. Secondly, data from problem to problem, even within the same
discipline, has to be transferred manually. The situation is similar to having a road system without
intersections for transferring from one road to the other road. When you reach an intersection you
walk off from one vehicle and take the other vehicle on the other road.
The manual transfer of data combined with extensive initial data gathering and input preparation
involve much mundane work on the part of the engineer. This tends to discourage the engineer from
application of the existing programs unless the problem is complex or sufficiently large. Several
problems require more than one run of the program to enable the engineer to zero-In on the solution.
Repeated effort in data transfer, data gathering and input preparation adds to the cost of the program
utilization and often the result is more expensive than the old fashioned slide rule solution.
This brings us to the problem of economics as related to the cost of computers.
In spite of all the progress in programming, it is still time-consuming and expensive. Actually
at present programming has not advanced at the same rate as developments in hardware. We are unable
to estimate the magnitude of effort involved in coding and algorithms for all the building disciplines.
As a point of reference, the structural design and analysis system in ICES called STRUDL comprises al-
most ten million characters of coding and data. As you know, the structural component is just a frac-
tion of the entire building design. We do not know how many characters of data would be required to
describe completely a building design if it were stored in a computer. When we consider a complete
computer-aided design system, no one is prepared to answer questions such as:
"What is the cost of suitable hardware?"
"How many man years will it cost to take to develop suitable software?"
"How much will it cost?"
788
The reason for 'no' or vague answers is that based on the present capabilities, the cost of such a
computer-aided design system will be out of this world; beyond the economical reach of most of the design
organizations •
Why should we be using computers in the building industry?
"The computers are not economical at the moment".
"Programming is difficult and time consuming".
"The building industry is too disorganized to be automated".
Having said all that, the question is "why should we be using computers in the building industry?".
The answer to this question involves awareness of the challenges of the future rather than the
handicaps of the present.
The key factor of the challenge of the future is the expected growth of population. Next to food,
shelter is a necessity for human survival. The building industry has to plan to meet the critical de-
mands of the future.
The world population is expected to almost double by the year and have a 30% increase by the
year . The following figures for increase in population are based on conservative estimates:
(Figures in millions)
2 000
World
3,700
4,600
6,900
U.S.A.
210
240
310
Developed Countries
1,060
1,350
1,570
Less Developed Countries
2,640
3,250
5,530
(Developed countries include: North America, Soviet Union, Australia, New Zealand, Europe and Japan.
Less developed countries include: East Asia (excluding Japan), South Asia, Africa, Latin America and
others . )
Now you can translate this population growth in the demand for housing, schools, areas of business,
hospitals and recreation facilities. All of this adds up to a heavy demand or may be critical shortage
for building construction facilities.
One can look at this problem from a different perspective. In only four cities had a popula-
tion of one million or more. By , the number had increased to nineteen cities. By , 141 cities
had a population of more than one million people. The past trend has shown that the population expan-
sion has taken place around the cities. If this trend continues and if population doubles by the year
, by that time we will have to double the existing cities. We will have to build one more London,
one more Rome, one more Tokyo, one more New York, one more Chicago, one more Los Angeles and so on.
It is expected that by the year 2 000 the United States will probably have three megapolises, one
on the East Coast which will extend from Boston to Washington; maybe from Portland, Maine to Portsmouth,
Virginia and might contain almost 25% of the United States population, that Is about 80 million people.
The second megapolis will be concentrated around the Great Lakes area which may stretch from
Chicago to Pittsburg and possibly also north to the Toronto region of Canada--thereby including Detroit,
Toledo, Cleveland, Akron, Buffalo and Rochester. This megapolis seems likely to contain more than one-
eighth of the United States population, about 40 million people.
The third megapolis on the Pacific Coast would probably stretch from San Diego to Santa Barbara,
ultimately from San Francisco to Santa Barbara and would contain one-sixth or about 20 million people.
789
Let us continue to look at this problem from a different perspective. In the last 70 years in
this country, the consumption and therefore production of goods and services has almost doubled every
15 years. If this rate of increase continues, we will see one more doubling by the year and
another doubling by the year . As you well know, both production as well as consumption of goods
and services will require additional construct ion--that is factories, stores, warehouses and offices.
With progress in technology, we can automate production of goods, introduce efficiencies in production
and services, but up to now we have no plans for automating the consumption.
Let us continue to look again from a different perspective, this time the growth in educational
facilities .
In spite of extensive educational facilities here, there are estimated to be about 25 million
adults, 18 years of age or over, in the United States with less than eighth grade education. This has
created the problem of unemployable unskilled labor. 15% of the unemployed in the three major ghetto
areas in New York City have never had a white collar job at any time. On the other hand, 507e, of job
vacancies in the New York City area are for white collar workers. It is estimated that in 10 years only
47o of the employment market will be open to the unskilled. We will need more schools, colleges and
universities to educate people, not for the sake of education alone, but to enable them to hold jobs
and provide services for the future.
In some of the less developed countries, the educational system is either non-existent or minimal.
We have educational problems here, but our problems are similar to a shot from a toy pistol as compared
to the educational explosion which is going on in countries such as Africa, Asia, Arabia, and Latin
America. These nations feel that it is crucial to their development to have a basic educational system.
Well over half a billion people must be taught to read, write and master simple computational skills.
Hundreds of millions of people must be brought to accept new practices in agriculture, health and home
management .
The occupational skills of millions must be brought up to the requirements of new Industries,
public works and service occupations which are waiting to be created. These educational facilities
will again require buildings and more buildings.
Medical facilities are being improved constantly, which have increased the life span for people
throughout the world. We will need more hospitals, not only because of increased population, but also
for more people, as, hopefully, people will be living longer.
In the Colonial times, the buildings were planned for a life of no less than 100 years. The re-
cent construction, it is hoped, will last at least 30 years. In other words, a building completed
today, will have to be replaced by the year 2 000 if not sooner.
Finally, in this respect we know that as societies become more industrialized, people work less
and less on their job, and we tend to have a leisure-oriented society. It is expected that by the year
, working hours will be reduced from the present, about hours per year, to per year. In
such a leisure-oriented society, one could spend kO°L of one's day on vocation, 407=, on avocation and
20% on neither, just relaxing. The increased availability of time for leisure, avocation and relaxa-
tion will require increase in buildings for recreation and travel.
At present, apart from lack of money, the second critical shortage is of design and construction
personnel for the building industry. If we are planning to meet the critical needs of the future, we
have to utilize efficiently all the available resources. Our plans will have to include the potential
of computers to solve the communication problems of the building industry.
What should be done to plan for the future?
In order to plan for the future and avoid making mistakes, we must begin to anticipate earlier
than we have in the past the problems of the future. Some of them already are becoming quite clear,
and their impact can be expected to be so enormous as to require a long lead time for assessment and
preparation.
A look at the history of scientific and technological change will help us understand that in-
adequately perceived goals may be of greater significance than any possibilities we can foresee. We
must alter our standard approach to the future in a way that will enable us to cope with what cannot
be anticipated. At the same time, however, we must also try to anticipate as much as possible in
order to provide a rational framework for our expectations.
First of all, we do not have to be discouraged by the present cost and capabilities of the com-
puter.
790
In the past, computer performance has increased by a factor of 10 in every two or three years, and
this is considered a consfervative estimate. If computer capabilities were to continue to increase by
a factor of 10 every , two or three years until the end of the century, then all current concepts about
computer limitations will have to be reconsidered. Even if the trend continues for only the next decade
or two, the improvements over current computers will be factors of thousands to millions. If we add the
likely enormous improvements in input /output devices, programming and problem formulation and better
understanding of the basic design process, the estimates of improvement will be conservative. Even if
the rate of change slows down by several factors, there will still be room in the next thirty years for
overall improvement of some 5 to 10 orders of magnitude. Therefore, it is necessary to ignore often
meaningless or non-rigorous statements such as "we are at present limited by the computer".
The computer costs will continue to decrease while the manpower cost will increase rapidly. What
might seem uneconomical today, will be economical tomorrow, and a necessity for survival day-after-
tomorrow.
With improvement in the computer hardware and reduction in cost, one can foresee that the computer
utility industry will become as fundamental as the power industry. A large central processor will
handle information at a low unit cost just as a large central generator produces electricity at a low
unit cost. It will be cheaper to make use of this central utility than it is for each individual to
have his own generator.
With the development of telecommunication for computers whereby engineers can use low cost termi-
nals in their offices, it will be possible to help in the matter of locational fragmentation existing
at the moment .
We have already established the critical needs of the building industry. We hope that the com-
puter technology will progress fast enough to enable us to satisfy our requirements. While suitable
hardware is being developed, we will have to work on development of a Computer-Aided Design System to
solve problems of communication. Such a system will have several subsystems, but all of these will
share a common data file for the entire project stored on a secondary storage.
It is now up to us to develop such a system based on our imagination, expectations and capabilities.
From the stage of problem solving we have to progress to the concept of communication as a key to com-
puterized building design system.
We also have to recognize the necessary components or requirements of such a system.
The most important component of the system is people: People or designers. Because of present
inadequate understanding of the design process the computer-aided building system must allow the de-
signers to make all the critical decisions involved in the use of the system. The real danger in
developing a computer-aided design system is not that it will produce poor design, but that it may
fail to consider the human element of the system and force the user into rigid procedure in its use,
thereby either discouraging use of the system or stifling any creative aspects of design.
Most important, we have to analyze and increase our understanding of the basic design process in
order to utilize full potential of the computer-aided design system.
When computers first became available, the tendency was to program all of the approximate methods
of analysis that have been designed for hijman users. It was only when reformulating the process that
engineers realized that the appropriate way to attack the problem of computerized analysis was to use
all the abilities of the computer and program rigorous method of analysis.
As you can appreciate, development of a computer-aided design system will be an expensive and time
consuming task. We cannot afford any duplication since we have limited resources and are racing against
time. It is therefore necessary that all of you who are interested in the building industry should
pool your resources and join in a common effort in developing such a computer-aided design system.
The sheer intensity of the future demand makes it ridiculous to compete in this task on a pro-
fessional, regional, or national basis. We can utilize our resources more efficiently by establishing
international cooperation on what appears to be a common. goal. You can achieve this objective by
joining, supporting and leading existing cooperative efforts.
How much progress will be made to meet the problems of tomorrow will depend on you.
791
Candid Views of the Participants at the Symposium Banquet
F. H. Bridges, Pr esi dent of ASHRAE ,
Master of Cermonies of the banquet.
Banquet head table from left to right: A. T. Boggs, ASHRAE; Mrs. P. R.Achenbach;
F. H. Bridgers, ASHRAE; S. Daryanani, APEC;P. R. Achenbach, NBS ; J. M. Ayres,
President, APEC;Mrs. F. J. Powell; and T. Kusuda, NBS. (Not shown at the left end
of the table are Mrs. T. Kusuda and F. J. Powell, NBS . )
Japanese delegation with Dr . T. Kusuda, Chairman
of the Program Committee and Mrs. Kusuda.
K. Kimura, Head of delegation, is shown at the
center of front row.
793
I
G. L. Gupta, Building R esearch Institute,
India; Mrs. G. L. Gupta; T. Y. Sun,
J. M. Ayres, and K. Parks of Ayres,
Cohen & Hayakawa and Julia Szabo, ASHRAE
(left to right).
I. Hogland, Royal Institute of Technology, Sweden;
A. T. Boggs, ASHRAE; P. G. Down, Oscar Faber
and Partners, England; C. W. Phillips, NBS;
J. B. Chaddock, Duke University; and E. N. Van
Deventer, National Building R esearch Institute,
South Africa (left to right).
J. J. Anquez and L. G. Bertolo, CSTB, France;
K. Fitzner, LTG Lufttechnis che Gmbh, West
Germany; W. K. Thomas, Thomas -Young Associates ;
R. F. Mehnert, B. H. Silber stein As sociates ; and
J. L. Norris, Long Island Lighting Company (left
to right).
F. J. Powell, NBS, Vice Chairman, Symposium;
Mrs. F. J. Powell; R. H. Tull, ASHRAE; P. R.
Achenbach, NBS; and Mrs. P. R. Achenbach
(left to right).
794
Mrs. G. L. Gupta; N. Gulati, D. C. Government;
G. L. Gupta, Buildiog R esearch Institute, India;
Mrs. N. Gulati; Mrs. A. Chawla;A. Chawla, D. C.
Government; Valerie Butler, Nash Love Associates;
and N. K. Khosla, Enviro-Management & Research
(left to right).
C. W. Phillips, NBS, Chairman of Arrangements
Committee, (left), and F. Clain, COSTIC, France.
A
PR
E. N. VanDeventer, National Building R esearch
Institute, South Africa; Sarah Torrence, NBS; and
E. Christopher son, Danish Building R es ear ch
Institute (left to right).
E. M. Barber, NBS; A. R. Paradis, Dynamic
Graphics Inc. ; Mrs. A. R. Paradis; N. La
Courte, ASHRAE; B. W. Ward, Britt Alderman,
Jr. ; L. G. Spielvogel, Inc. ; andH. K. Varma,
North Carolina A h T State University (left to
right).
LIST OF REGISTERED ATTENDEES
J. T. Adams
Union Carbide Corp. - Nuclear Division
Post Office P - Building K-lOOl
Mail Stop 157
Oak Ridge, Tennessee
S. Agerbek
The Ralph M. Parsons Co., Los Angeles, Cal.
Santa Bianca Drive
Hacienda Heights, California
J. R. Akerman
University of Michigan
Van Dusen Drive
Ann Arbor, Michigan
W. R. Anderson
Bureau of Reclamation
Department of Interior
Denver, Colorado
C. A. Alders
Texas Electric Service Company
P. 0. Box 970
Fort Worth, Texas
J. M. Alvord
Alvord and Swift, Incorporated
60 East 42nd Street
New York, New York 10 017
D. F. Anderson
DeLeuw-Cather Company
955 L' Enfant Plaza, S.W.
Washington, D. C.
J. J. Anquez
C. S. T. B.
Avenue du Recteur POINCARE
Paris , France
N. Aratani
Architectural Department
Faculty of Engineering of Hokkaido
University
North-12, West-8
Sapporo, Japan
A. E. Arledge
Carrier Overseas Corporation
Carrier Parkway
Syracuse, New York
R. S. Arnold
Carrier Air Conditioning Company
Carrier Parkway
Syracuse, New York
E. G. Arntzen
Los Alamos Scientific Laboratory
P. 0. Box
Los Alamos, New Mexico
R. G. Attridge, Jr.
Ranco Controls Division
601 West Fifth Avenue
Columbus, Ohio
L. R. Axelrod
Powers Regulator Company, Systems Division
MacArthur Boulevard
Northbrook, Illinois
J. M. Ayres
Ayres , Cohen & Hayakawa
South Beverly Drive
Los Angeles, California
D. Bahnfleth
Heating, Piping, and Air Conditioning
10 South La Salle Street
Chicago, Illinois
C. H. Barcus
Professor of Architecture
Miami University
Westgate Drive
Oxford, Ohio
B. H. Barksdale
Hayes, Seay , Mattern & Mattern
P. 0. Box
Roanoke, Virginia
W. B. Barnard
Honeywell, Incorporated
Commercial Division
North Austin Avenue
Morton Grove, Illinois
C. Barton
Smith, Hinckman 6. Grylls Associates, Inc.
West Grand Boulevard
Detroit, Michigan
J. R. Beckum, P.E.
Vincent G. Kling & Associates
Arch Street
Philadelphia, Pennsylvania
G. Bees ley
DP&L Company
Commerce
Dallas, Texas
797
H. F. Behls
Sargent & Lundy
140 South Dearborn Street
Chicago, Illinois
W. F. Beiderman
American & Telegraph Company
32 Avenue of the Americas , Room
New York, New York
E. L. Bell
Hawkins & Anderson, Consulting Engineers
North Hamilton Street
Richmond, Virginia
A. G. Bendelius
Parsons, Brinckerhof f , Quade & Douglas, Inc
111 John Street
New York, New York
H. Benjamin
Surveyor, Nenniger & Chenevert , Inc.
de Maisonneuve Boulevard, West
Montreal 107, Quebec, Canada
L. M. Bent
Department of Public Works
301 Elgin Street
Ottawa, Ontario, Canada
L. G. Bertolo
C. S. T. B.
4 Recteur Poincare
Paris, France
J. J. Sevan
Philadelphia Electric Company
211 South Broad Street, 9th Floor
Philadelphia, Pennsylvania
L. D. Beverage
The Potomac Edison Company
Downsville Pike
Hagerstown, Maryland
A. Bijl
Architecture Research Unit
University of Edinburgh
55 George Square
Edinburgh, Scotland, UK EH 8 9JU
B. E. Birdsall
Ziel-Blossom & Associates, Incorporated
700 Valnut Street
Cincinnati, Ohio
W. P. Bishop
Joseph P. Wohlpart Associates
155 East 42nd Street
New York, New York
G. H. Blair
Honeywell, Incorporated
24-30 Skillman Avenue
Long Island City, New York
H. G. Blasdel
Department of Architecture
University of California
Berkeley, California
A. W. Boeke
Technische Hogeschool, Leerstoel
Klimaatregeling
Mekelweg 2, Delft
The Netherlands
A. T. Boggs
ASHRAE
345 East 47th Street
New York, New York
A. Boysen
National Swedish Institute for Building
Research
Box , S-102
Stockholm 27, Sweden
A. P. Brazzale
Post Office Department
Bureau of Facilities
Washington, D. C.
P. J. Breman
Union Carbide Corporation
P. 0. Box Y
Building -1
Oak Ridge, Tennessee
F. H. Bridgers
ASHRAE
213 Truman Street, N.E.
Albuquerque, New Mexico
R. E. Brigham
Department of Defense DIASA-3B
Pentagon
Washington, D. C.
C. Broder
Port of New York Authority
111 8th Avenue
New York, New York
G. Brown
Royal Institute of Technology
Stockholm 70, Sweden
R. S. Buchanan
ASHRAE
345 East 47th Street
New York, New York
798
S. R. Buchanan
Johnson Service Company
507 East Michigan Street
Milwaukee, Wisconsin
R. S. Bycraft
Department of Public Works of Canada
Design Branch, Mechanical Engineering
Division
Sir Charles Tupper Building
Ottawa 8, Ontario, Canada
J. H. Cansdale
ASHRAE
345 East 47th Street
New York, New York
J. D. Carson
Leo A. Daly Company
Connecticut Avenue, N.W.
Suite 712
Washington, D. C.
J. B. Chaddock
Duke University
Department of Mechanical Engineering
Durham, North Carolina
A. C. Chawala
D. C. Government
Department of General Services
Washington, D. C.
J. Y. Chini
IBM
Frederick Pike
Gaithersburg, Maryland
E. Christophersen
Danish Building Research Institute
Postgird
Copenhaven, Denmark
I. C. S. Chou
Mechanical Engineering Department
University of Hawaii
Honolulu, Hawaii
B. 0. Cingilli
Tennessee Valley Authority
Knoxville, Tennessee
F. Clain
Co. S. T. I. C.
9, Rue La Perouse
75 - Paris 16, France
J. T. Cleckley
Georgia Power Company
P. 0. Box
Atlanta, Georgia
L. B. eleven
State of Wisconsin
Bureau of Capitol Development
1 West Wilson Street
Madison, Wisconsin
I. L. Clunie
Nicholas Fodor and Associates, Ltd.
38 Charles Street, East
Toronto 5, Ontario, Canada
R. F. Cook
Westinghouse Electric Corporation
700 Braddock Avenue 7L27
East Pittsburgh, Pennsylvania
Z. Cumali
Consultants Computation Bureau
594 Howard Street
San Francisco, California
A. Curl
Space, Incorporated
Elm Street
Dallas, Texas
D. M. Curtis
Oscar Faber & Partners
18 Upper Marlborough Road
St. Albums, Herts, England
M. Dagenais
LaLonde Valois Lamarre Valois & Associates
615, rue Belmont
Montreal 101, P. Q.
Canada
B. Davis
Deere & Company
Manufacturing Engineering Department
Moline, Illinois
T. Davis
McGaughy , Marshal and McMillan
220 West Freemason Street
Norfolk, Virginia
L. 0. Degelman
Associate Professor of Architecture Engin.
Pennsylvania State University
101 Eng "A" Building
University Park, Pennsylvania
J. DeGuise
P. DeGuise & Associates
St. Laurent
Montreal, Quebec, Canada
P. DeGuise
P. DeGuise & Associates
St. Laurent
Montreal, Quebec, Canada
799
E. I. Diab
Letendre, Monti, Lavoie, Nadon
McGill College, Suite 530
Montreal, P. Q. , Canada
H. B. Dickenson
Hayes, Seay, Mattern & Mattern
P. 0. Box
Roanoke, Virginia
C. Dorgan
Wright-Patterson Air Force Base
Ohio
G. Dombusch
Columbia Gas of Maryland
1 South Potomac Street
Hagerstown, Maryland
P. G. Down
Oscar Faber & Partners
18 Upper Marlborough Road
St. Albans
Herts, England
G. R. Dunham
Corps of Engineers - Sacramento District
650 Capital Mall - Room
Sacramento, California
M. R. Edwards
Washington Gas Light Company
H Street, N.W.
Washington, D. C.
G. Engholm
GARD/GATX
North Natchez Avenue
Niles, Illinois
P. Euser
Technisch Physische Dienst
TNO-TH
Stieltjesweg 1
P.O.B. 155
Delft, Netherlands
H. E. Faller
Harold E. Faller & Associates
South Salcedo Street
New Orleans, Louisiana
K. H. Faller
Harold E. Faller & Associates
S. Salcedo Street
New Orleans, Louisiana
T. Fehrenbacher
McDonnell Douglas Automation Corporation
Building 105, Level 4, Post D2
St. Louis, Missouri
D. Fitzgerald
Heating & Ventilating Research Association
Old Bracknell Lane
Bracknell Berks RG12 4AH, U. K.
K. Fitzner
LTG Luf ttechnische Gmbh
D-7 Stuttgart 40, Werner Str.
Postfach 39, West Germany
D. Fletcher
Detroit Edison Company
Second Avenue
556 Service Building
Detroit, Michigan
S. R. Fogleman
Sam R. Fogleman Associates, Consulting
Engineers
Ponce de Leon Avenue
Rio Piedras, Puerto Rico
C. T. Fox
Gas-Fired Products, Incorporated
305 Doggett Street, P. 0. Box
Charlotte, North Carolina
E. T. Fredricks, Jr.
Gritschke & Cloke, Incorporated
221 North LaSalle Street
Chicago, Illinois
D. Freeling
Post Office Department
12th NW & Pennsylvania
Washington, D. C.
J. E. Fromm
K07/025
IBM Research Laboratory
Monterey and Cottle Roads
San Jose, California
C. A. Fry, P.E.
Chief Mechanical-Industrial Engineer
Buchart-Horn (Consulting Engineers &
Planners)
40 South Richland Avenue
York, Pennsylvania
Y. Fukushima
Shin Nippon Air Conditioning Company, Ltd.
4-2, Hongoku-cho , Nihombashi, Chuo-ku
Tokyo, Japan
D. W. Galehouse
Automated Construction Technology, Inc.
P. 0. Box 103
Dayton View Station
Dayton, Ohio
800
J. p. Galloin
Carrier Overseas Corporation
Carrier Parkway
Syracuse, New York
V. M. Garcia
School of Architecture
University of Puerto Rico
P. 0. Box UPR Station
Puerto Rico
J. J. Gat to
Westinghouse Tele-Computer Systems Corp.
Ardmore Boulevard
Forest Hills, Pennsylvania
P. G. Lavoie
Lorrain & Gerin-Lavoie Consulting Engineers
0. Jean Talon
Montreal 308
P. Quebec, Canada
D. S. Gill
DeLeuw-Cather & Company
955 L'Enfant Plaza, S.W.
Washington, D. C.
L. Gill
Mountain Fuel Supply Company
Salt Lake City, Utah
T. Gooch
Benham-Blair & Affiliates
North Grand Boulevard
Oklahoma City, Oklahoma
M. D. Good
Los Angeles Department of Water & Power
111 Hope Street, North
Los Angeles, California
H. D. Goodman
Joseph R. Loring & Associates
Two Pennsylvania Plaza
New York, New York
R. A. Gordon
Cornell, Howland, Hayes & Merryfield
Western Boulevard
Corvallis, Oregon
K. M. Graham
Southern California Gas Company
P. 0. Box Terminal Annex
Los Angeles, California
0. Granlund
Ingenjorbyra Olof Granlund Antti Oksanen
Elisabetsgatan 19 A 5
Helsingfors 17, England
M. H. Gray, III
Whirlpool Corporation
Higliway 41 North
Evansville, Indiana
K. J. Guion
Smith, Hinchman & Grylls Associates, Inc.
West Grand Boulevard
Detroit, Michigan
N. K. Gulati
Sanitary Engineering Department
D. C. Government
B29 E Street, N.W., Room 945
Washington, D. C.
C. L. Gupta
CSIRO
Division of Building Research, Hyhelt
P. 0. Box 56
Australia VIC
E. F. Gurka, Jr.
U. S. Postal Service
12th & Pennsylvania Avenue, N.W.
Washington, D. C.
K. Hagimoto
Mitsubishi Heavy Industries, Ltd.
No. 1, Takamichi, Iwatsuka-cho , Nakamura-ku
Nagoya, Japan
H. J. Haebler , Jr. , P.E.
Luther M. McLeod and Associates
200 East Joppa Road
Towson, Maryland
N. E. Hager, Jr.
R 6i D Center, Armstrong Cork Company
Columbia Avenue
Lancaster, Pennsylvania
R. W. Haines
Collins Radio Company
Dallas, Texas
A. Handshy
Bank Building Corporation
Hampton Avenue
St. Louis, Missouri
J . J . Harmon
Carrier Air Conditioning Company
Bentridge Lane
Richmond, Virginia
G. N. Hashmi
Ellerbe Architects
333 Sibley Street
St. Paul, Minnesota
801
R. J. Hatwell
U. S. Coast Guard Headquarters
400 7th Street, S.W.
Washington, D. C.
T. Haw, III
Chrysler Corporation
P. 0. Box
Detroit, Michigan
J. E. Hays
Naval Facilities Engineering Command
Electronic Facilities Support Division,
Code 044
Washington, D. C.
K. J. Hazell
J. L. Richards 6i Associates , Ltd.
864 Lady Ellen Place
Ottawa, Ontario, Canada
J. B. Headrick
Dallas Power and Light Company
Commerce Street
Dallas, Texas
M. A. Hertzberg, P.E.
M. A. Hertzberg, Consulting Engineers
Sugarbush Village
Warren, Vermont
J. B. Hoaglund
ITT
320 Park Avenue
New York, New York
I. Hoglund
The Royal Institute of Technology
Division of Building Technology
S-100 44 Stockholm 70, Sweden
G. M. Hollander _ ;
Veterans Administration
810 Vermont Avenue, N.W.
Washington, D. C.
R. F. Hughes
Earl Walls Associate
La Jolla Boulevard
La Jolla, California
R. L. Hughes, Jr.
ENTCO
5 East 23rd Street
Baltimore, Maryland
E. Isfalt
The Royal Institute of Technology
Stockholm 70, Sweden
H. Ishino
Waseda University (Graduate School)
4-170, Nisi-Ogikubo , Shinjuku-ku
Tokyo, Japan
J. H. Jacobs, Jr._
Chas. T. Main, Incorporated
441 Stuart Street
Boston, Massachusetts
G. F. Jacobson
Headquarters PACAF
Aalapapa Drive
Kailua, Hawaii
J. S. Jarolim
Army and Air Force Exchange Service
ATTN: CSXPT-2
Dallas, Texas
F. Jennings
Walter Kidde Constructors, Incorporated
19 Rector Street
New York, New York
J. W. Jones
Ohio State University
206 West 18th Avenue
Columbus, Ohio
J. E. Kampmeyer, P.E.
Robert E. Lamb, Incorporated
Valley Forge Industrial Park
Valley Forge, Pennsylvania
J. Y. Kao
National Institutes of Health
Room , Building 13
Bethesda, Maryland
M. B. Kassay
Sahara, Incorporated
29-28 41 Avenue
Long Island City, New York
E. R. Kaufman
U. S. Postal Service - San Francisco
Regional Office
631 Howard Street
San Francisco, California
H. W. Keil
Alvord and Swift
60 East 42nd Street
New York, New York
N. K. Khosla
Enviro-Management & Research, Incorporated
901, 8th Street, N.W.
Washington, D. C.
802
C. Kimball.
Carrier Corporation
Carrier Parkway
Syracuse, New York
T. Kimoto
Oversears Industry Research Center
4-4, Kojimachi, Chiyoda-ku
Tokyo, Japan
K. Kimura
Waseda University (Associate Professor)
4-170, Nishiokubo, Shinjuku-ku
Tokyo, Japan
G. R. Kinzer
Johns-Manville Products Corporation
Research & Engineering Center
Manville, New Jersey
M. B. Kispert
Ellerbe Architects
333 Sibley Street
St. Paul, Minnesota
W. J. Kissell
Mountain Fuel Supply Company
180 East First South Street
Salt Lake City, Utah
S. H. Klein
Department of National Defense, Canada
C. F. H. Q. - DCEDE - Ottawa 4
Ontario , Canada
J. L. Kmetzo, P.E.
Syska U Hennessy, Incorporated
144 East 39 Street
New York, New York
R. Kobrick
Seelye, Stevenson, Valve, & Knecht
99 Park Avenue
New York, New York
G. Koch
IBM
Real Estate & Construction Division
Westchester Avenue
White Plains, New York
A. Kokalari
American-Standard, Incorporated
P. 0. Box
New Brunswick, New Jersey
Y. Konishi
The Shimizu Construction Co., Ltd.
Research Laboratory
2-1, Takara-Chou, Chou-Ku
Tokyo , Japan
A. Konoike
Kantogakuin University
Mutsuura-cho
Kanazawa-Ku, Yokohama, Japan
C. L. Koppenhaver
Gilbert Associates, Incorporated
P. 0. Box
Reading, Pennsylvania
R. Kramer
Honeywell, Incorporated
North Austin Avenue
Morton Grove, Illinois
S. F. Krogstad
AEDC
Arnold A. F. Station
Tennessee
D. A. Krot
Carnegie Mellon University
Schenley Park
Pittsburgh, Pennsylvania
S. Kuramochi
Taisei Construction Company, Ltd.
No. 2-1, Kyobashi, Chuo-ku
Tokyo , Japan
F. Kurihara
P. T. Morimura & Associates
Consulting Mechanical & Electrical
Engineers
1-2-9, Yoyogi, Shibuya-ku
Tokyo, Japan
C. F. Kwok
Veterans Administration
810 Vermont Avenue, N.W.
Washington, D. C.
C. LaBrecoue
P. DeGuise & Associates
St. Laurent
Montreal, Quebec
Canada
N. A. LaCourte
ASHRAE
345 East 47th Street
New York, New York
R. Lahmon
Eastman Kodak
Kodak Park
Rochester, New York
J. T. H, Lammers
University of Technology, Building Dept.
Building Wen S, Room
Eindhoven
The Netherlands
803
L. L. Lampert
Buerkel & Company, Incorporated
129 Maiden Street
Boston, Massachusetts
S . Larm
AB Svenska Flaktf abrlken
S-104 60 Stockholm
Sweden
T. A. Lawand
Brace Research Institute
MacDonald College
Ste. Anne de Behlevue
Quebec, Canada
K. G. Lawrence
Philadelphia Electric Company
211 South Broad Street - 9th Floor
Philadelphia, Pennsylvania
J. DeBaut
Electricite de France
Les Renavudieres Eludes et Recherches
77 Ecuelles, France
H. S. Lewis
Jaros , Baum & Bolles
345 Park Avenue
New York, New York
B. G. Liebtag
Duquesne Light Company
435 Sixth Avenue
Pittsburgh, Pennsylvania
T. D. Lin
Portland Cement Association
Old Orchard Road
Skokie, Illinois 600 76
E. J. Leon
National Research Council of Canada
Montreal Road Laboratories
Ottawa 7, Ontario
Canada
M. Lokmanhekim
General American Research Division of GATX
North Natchez Avenue
Niles, Illinois
J. L. Loomis
Human Performance Research Laboratory
Pennsylvania State University
University Park, Pennsylvania
T. Looney
McFall and Konkel Consulting Engineers, Inc.
South Clermont Street
Denver, Colorado
R. P. Lortie
Associated Engineers, Incorporated
670 West Sixth Street
Winston-Salem, North Carolina
I. Lotersztain
Bouwcentrum Argentina
Cangallo 700 esq. Maipu
Buesnos Aires, Argentina
N. M. Love
Nash M. Love Associates
901 8th Street, N.W.
Washington, D. C.
W. H. Loyd
Bender Burrell Associates
P. 0. Box 13
Camp Hill, Pennsylvania
F. F. Lusby, Jr.
Lusby & Company, Consulting Engineers
300 North Potomac Street
Hagerstown, Maryland
E. L. MacFerran
Tennessee Valley Authority
Knoxville, Tennessee
H, D. MacPhee
Department of Public Works of Canada
P. 0. Box , Halifax South Postal
Station
Halifax, Nova Scotia, Canada
C. J. R. McClure
Charles J. R. McClure & Associates, Inc
Old Olive St. Rd.
St. Louis, Missouri
A. F. McCrea
Robertshaw Controls Company
Byrd Avenue
Richmond, Virginia
D. McCurdy
Ontario Hydro
Yonge Street
Willowdale, Ontario, Canada
R. W. McDonald
Carolina Power & Light Company
Box
Raleigh, North Carolina
R. W. McKinley
PPG Industries
1 Gateway Center
Pittsburgh, Pennsylvania
804
W. C. McMurry
American Gas Association
Wilson Boulevard
Arlington, Virginia
D. McNamara
Ministry of Public Buildings & Works
Cleland House, Page Street
London SWl , England
W. L. McNamara
ADI Limited
P. 0. Box 4A, Fredericton
New Brunswick, Canada
J. C. Magnussen
Honeywell , Inco rpo rated
Fourth Avenue South
Minneapolis, Minnesota
Jeet Mahal
Vosbeck, Vosbeck, Kendrick and Redinger
720 North St. Asaph Street
Alexandria, Virginia
Fiji Maki
Nikken Sekkei Ltd.
Planners /Architects /Engineers
2-38, Yokobori, Higashi-ku
Osaka, Japan
J. F. Malarky
PPG Corporation
One Gateway Center
Pittsburgh, Pennsylvania
Stanley Mankowski
The Austin Company
450 West First Avenue
Roselle, New Jersey
Seprl Marcq et Roba
Consulting Engineers
Boulevard Leopold II
Brussels, Belgium
John W. Markert
General Services Administration
18th and F Streets, N.W.
Room
Washington, D. C.
H. J. Martin, Jr.
Public Service Electric and Gas Company
80 Park Place, Room
Newark, New Jersey
Robert L. Mason
Texas Technical University
Mechanical Engineering Department
P. 0. Box
Lubbock, Texas
S. Mass on
Perkins and Will Service Company, Inc.
Washington, D. C.
Koichi Matsuda
Hitachi Plant Engineering & Construction
Company, Ltd.
1-13-2, Kita-Otsuka, Toshima-ku
Tokyo , Japan
T. Mazuchowski
Smith, Hinchman & Grylls Association, Inc.
West Grand Boulevard
Detroit, Michigan
Robert W. McKinley
PPG Industries
One Gateway Center
Pittsburgh, Pennsylvania
Ralf F. Mehnert
Benjamin H. Silberstein Associates
21 Hanover Place
Hicksville, New York
Laheri Mehta
S&H Information Systems, Incorporated
144 East 39th Street
New York, New York
H. T. Mei
Lamar State College of Technology
Box , Lamar Station
Beaumont, Texas
R. F. Meriwether
Ross F. Meriwether & Associates, Inc.
N. E. Loop 410
San Antonio, Texas
S. R. Michaelis
Perkins & Will Service Company, Inc.
Washington, D. C.
S. Miletta
Walter Kidde Constructors, Incorporated
19 Rector Street
New York, New York
James R. Miller
Westinghouse Tele-Computer Systems Corp.
Ardmore Boulevard
Pittsburgh, Pennsylvania
E. C. Mills
Philadelphia Electric Company
211 South Broad Street
Philadelphia, Pennsylvania
805
Wayne A. Mills
Director of Government Sales
Washington Gas Light Company
H Street, N.W.
Washington, D. C.
Dale R. Missler
Hellmuth, Obata & Kassabaum
315 North 9th Street
St. Louis, Missouri
G. P. Mitalas
National Research Council
Building Research Division
Ottawa, Ontario, Canada
H. G. Mitchell
The Electricity Council
Trafalgar Buildings, 1
Charing Cross
London, S.W.I, England
Eiji Miyaji
The Shimizu Construction Company, Ltd.
2-1, Takara-cho, Chuo-ku,
Tokyo , Japan
Raymond J. Moss
IBM-Real Estate Division
Westchester Avenue
White Plains, New York
D. J. Mosshart
Limbach Company
Four Gateway Center
Pittsburgh, Pennsylvania
W. H. Mueller
Indianapolis Power & Light Company
25 Monument Circle
Indianapolis, Indiana
Jim Mullen
Lennox Industries, Incorporated
E. Linn
Marshalltown , Iowa
G. Mullins
Brown, Davis, & Mullins, Associates
Champaign, Illinois
J. Manzo
Vollmer Associates
P. 0. Box 407
Alexandria, Virginia
R. Muralidharan
General Electric Research & Development
Center
Building 37, Room 615, P. 0. Box 43
Schenectady, New York
Mr. Jerry Myers
Oklahoma Natural Gas Company
Post Office Box 871
Tulsa, Oklahoma
Kermit B. Myers
Mechanical Engineering Department
Iowa State University
Ames, Iowa
Yasuaki Nakazawa
Kyoto Technical University
Matsugasaki, Sakyo-ku, Kyoto, Japan
L. W. Nelson
Honeywell, Incorporated
4th Avenue, South
Minneapolis, Minnesota
G. Newton
Huf sev-Nicolaides Associates, Incorporated
215 Malaga Avenue Coral Gables
Miami, Florida
Y. Nishi
John B. Pierce Foundation Laboratory
290 Congress Avenue
New Haven, Connecticut
Soren F. Normann
DERAC Consultants, Incorporated
South East 56th
Mercer Island, Washington
J. T. Norris
Long Island Lighting Company
250 Old Country Road
Mineola, New York
0. J. Nussbaum
Halstead & Mitchell
Division of Halstead Industries, Inc.
Zelienople, Pennsylvania
Garfield A. Nuttall
Lakehead University
240 Van Horne Street
Thunder Bay, Ontario, Canada
U Tin Nyo
Berger Association Incorporated
Market Street
Camp Hill, Pennsylvania
Willard Oberdick
Smith, Hinchman & Grylls
University of Michigan
Ottawa
Ann Arbor, Michigan
806
R. H. O'Brien
C-K Engineering Company, Incorporated
Paulison Avenue
Clifton, New Jersey
Kiyoshi Ichifuji
The Faculty of Engineering
Hokkaido University
Sapporo, Japan
Tim 0' Connor
Inatome & Associates, Incorporated
West Nine Mile Road
Oak Park, Michigan
Ferenc Oezvegyi
Sulzer Brothers Limited
Winterthur, Switherland
Shogo Ogasawara
Sanki Engineering Company, Ltd.
1-10, Yuraku-cho, Chiyoda-ku
Tokyo, Japan
Toshio Okajima
A.C. Martin & Associates
Union Bank Square
Los Angeles, California
Yasukazu Okuda
Nikken Sekkei Ltd.
1-4-27, Koraku, Bunkyo-ku
Tokyo, Japan
Lowell B. Orange
Sacramento , Municipal Utility District
P. 0. Box
Sacramento, California
J. M. Owendoff
U. S. Air Force
Headquarters Aerospace Defense Command
(DEEEN)
ENT Air Force Base, Colorado
D. F. Owens
John Graham & Company
Mt. St. Helens Place, South
Seattle, Washington
Ferenc Ozvegyi
Sulzer Brothers Ltd.
Switzerland/Winterhur
W. P. Palmer
Peter F. Loftus Corporation
900 Chamber of Commerce Building
Pittsburgh, Pennsylvania
T. E. Pannkoke
Northern Illinois Gas Company
P. 0. Box 190
Aurora, Illinois
A. R. Paradis
Dynamic Graphics Incorporated
Dwight Way
Berkeley, California
T. V. Paranilam
Albert Kahn Associates, Incorporated
345 New Center Building
Detroit, Michigan
Kyoung Park
Ayres, Cohen £i Hayakawa
South Beverly Drive
Los Angeles, California
Gul Paryani
Reynolds , Smith and Hills
Boulevard Center Drive
P. 0. Box
Jacksonville, Florida
J. M. Patton
Sales Engineer
Mississippi Power Company
P. 0. Box
Gulfport, Mississippi
F. W. Paul
Carnegie-Mellon U.
Pittsburgh, Pennsylvania
Ifan Payne
University of Maryland
College Park, Maryland
C. 0. Pedersen
University of Illinois
130 Mechanical Engineering Building
Urbana, Illinois
R. E. Ferryman
Sandia Corporation
P. 0. Box
Albuquergue, New Mexico
J. A. Pettineo
Philadelphia Electric Company
900 Sansom Street
Philadelphia, Pennsylvania
H. M. Philippi
Atomic Energy of Canada Ltd.
Chalk River, Ontario, Canada
807
H. Harry Phipps
Energy Systfems Consultants
Sea Gull Drive South
St. Petersburg, Florida
E. D. Plociennik
Robertshaw Controls Company
Box 178
King of Prussia, Pennsylvania
F. E. Polk
Naval Facilities Engineering Command
Electronic Support Division
Code 044C
Washington, D. C.
Leo Pop
Ontario Hydro, Sales Division
620 University Avenue
Toronto, Ontario, Canada
G. W. Pozeck
General Services Administration
Public Buildings Service
Region 5
219 South Dearborn Street
Chicago, Illinois
H. E. Puttbach
Log Etronics Incorporated
Dryomatic Division
Electronic Drive
Springfield, Virginia
W. J. Radle
Airtemp Division
Chrysler Corporation
P. 0. Box
Dayton, Ohio
F. M. Ramsay
Post Office Department
Bureau of Facilities
Washington, D. C.
David Ramsey
Herman Blum Consulting Engineers, Inc.
Elm Street
Dallas, Texas
A. S. Ratra
Washington Gas Light Company
H Street, N.W.
Washington, D. C.
J. A. Reese
The Trane Company
Pammel Creek Road
LaCrosse, Wisconsin
George Reeves
Edison Electric Institute
750 30 N.E.
New York, New York
S. W. Reid
Gilbert Associates, Incorporated
P. 0. Box
Reading, Pennsylvania
D. L. Richardson
Arthur D. Little, Incorporated
20 Acorn Park
Cambridge, Massachusetts
C. P. Robart, Jr.
Electric Heating Association, Inc.
437 Madison Avenue
New York, New York
J. B. Roberson
Southern California Edison Company
P. 0. Box 351
Los Angeles, California
Charles Robertson
Architecture Research Unit
University of Edinburgh
55 George Square
Edinburgh, Scotland, UK EH89JU
R. J. Rodde
Godwin C. Rogerson
General Services Administration
7th and D Streets, S.W.
Washington, D. C.
Richard J. Rodde
Associated Engineers, Incorporated
505 West Nebraska Avenue
Peoria, Illinois
B. T. Rogers
Los Alamos Scientific Laboratory
P. 0. Box
Los Alamos, New Mexico
Robert Romancheck
Pennsylvania Power & Light Company
901 Hamilton Street
Allentown, Pennsylvania
T. B. Romine
Romine and Slaughter, Incorporated
Collinsworth
Fort Worth, Texas
Roy Rose
Reynolds, Smith and Hills
Architects, Engineers and Planners, Inc.
Blvd. Center Drive, P. 0. Box
Jacksonville, Florida
808
Harvey Rosenhouse
American Standard Research Center
P. 0. Box
New Brunswick, New Jersey
Teddy Rosenthal
Wahlings Installationsutveckling AB
Mysingsvagen 5, Box 1
Danderyd 1. Sweden
R. V. Ross
Bucher Meyers and Association
First Avenue
Silver Spring, Maryland
Harold E. Rucks
Architects Hansen Lind Meyer
116 South Linn Street
Iowa City, Iowa
James E. Rucks
Architects Hansen Lind Meyer
116 South Linn Street
Iowa City, Iowa
Sam Sachs
Skidmore, Owings & Merrill
30 West Monroe
Chicago, Illinois
J. L. Salinsky
Sargent -Webster-Crinshaw & Folley
Erie Boulevard East
Syracuse, New York
R. Sandy
W. Hardy Craig & Associates Ltd.
Consulting Engineers
Victoria Park Avenue, Scarborough
Ontario, Canada
J. R. Sarver
Westinghouse Electric Corporation
Box Chatham Center Office Building
Pittsburgh, Pennsylvania
William A. Schmidt
Veterans Administration 08H
810 Vermont Avenue, N.W.
Washington, D. C.
G. R. Schmieding
Northern Natural Gas Company
Dodge
Omaha, Nebraska
J. R. Schneider
Sverdrup & Parcel and Associates, Inc.
800 North 12th Street
St. Louis, Missouri
Judith Schurek
Bell Canada
100 Wynford Drive, Room 415
Don Mills, Ontario
E. C. Schuster
Michigan Wisconsin Pipe Line Company
P. 0. Box 149
615 W. Moreland Boulevard
Waukesha, Wisconsin
Bob Scott
Bob Scott, Architect & Engineer
Cambridge Road
Marietta, Ohio
Gert K. A. Siggelin
American SF Products, Inc.
701 Palisade Avenue
Englewood Cliffs, New Jersey
Hector R. Seiglie, P.E.
Connell Associates, Incorporated
Post Office Box 677
Miami, Florida
Jashwant Shah
Roy C. Ingersoll Research Center
Borg-Warner Corporation
Wolf and Algonquin Roads
DesPlaines, Illinois
H. C. Shaner
Kling-Leopold , Incorporated
Consulting Engineers
121 North Broad Street
Philadelphia, Pennsylvania
C. L. Shearburn
Human Performance, Research Laboratory
The Pennsylvania State University
103 Human Performance Building
University Park, Pennsylvania
D. G. Scheatzle
Wright-Patterson Air Force Base
Ohio
S. M. Shefferman
Shefferman & Bigelson Company
Spring Street
Silver Spring, Maryland
J. Y. Shih
Powers Regulator Company
Systems Division
Mac Arthur Boulevard
Northbrook, Illinois
Tatsuo Shimizu
Suga Company, Ltd.
17-19 Shimbashi 6 Chome Minato-Ku
Tokyo, Japan
809
Jorge E. Sierra
Smith, Korach, Hayet, Lippack, Haynie &
Associates
721 N.W. 21st Court
Miami, Florida
Edward Simons
Consulting Engineer
P. 0. Box 945
Tiburon, California
Michael Skrzywan
Systems Simulation, Inc.
207 East 37th Street
New York, New York
C. C. Smith
Johnson Service Company
507 East Michigan Street
Milwaukee, Wisconsin
J. H. Smith
National Institutes of Health
Room , Building 13
Bethesda, Maryland
R. B. Smith
Jersey Central Power & Light Company
Madison Avenue at Punch Bowl Road
Morristown, New Jersey
H. V. Snively
Robertshaw Controls Company
Byrd Avenue
Richmond, Virginia
Clyde Somerset Jr.
Sherlock, Smith & Adams, Incorporated
P. 0. Drawer
Montgomery, Alabama
J. K. Sonsteby
Pennsylvania Power & Light Company
901 Hamilton Street
Allentown, Pennsylvania ■
L. G. Spielvogel
L. G. Spielvogel, Incorporated
Consulting Engineer
Wyncote House
Wyncote, Pennsylvania 5
J. H. Sporidis
Benbassat & Sporidis Company
Georgia Avenue
Silver Spring, Maryland
Eugene Stamper
Newark Coll. of Engineering
323 High Street
Newark, New Jersey
James L. Stephens
Brown and Root Incorporated
P. 0. Box 3
Houston, Texas 7
D. G. Stephenson
National Research Council
Building Research Division
Ottawa, Ontario, Canada
R. G. Stinson
John Graham & Company
5th Avenue
Seattle, Washington
W. F. Stoecker
University of Illinois
Urbana, Illinois
Takeshi Sugama
Takasago Thermal Engineering Co. Ltd.
St. Rd. Apartment A-13
Warminster, Pennsylvania
Tseng-Yao Sun
Ayres, Cohen & Hayakawa
South Beverly Drive
Los Angeles, California
P. L. Sundberg
Consolidated Engineers, Incorporated
South 72nd Avenue
Omaha, Nebraska
G. C. Rocerson
General Services Administration
7th and D Streets, S.W.
Washington, D. C.
Sazuku Tanaka
Kajima Corporation
2-19-1 Tobstakyu
Chofu, Tokyo, Japan
B. Taylor
Minneapolis Gas Company
733 Marquette Avenue
Minneapolis, Minnesota
Leonard H. Taylor
Southern Technical Institute
Huntington Drive, N.W.
Marietta, Georgia
Hideo Teraguchi
Ayres , Cohen & Hayakawa
South Beverly Drive
Los Angeles, California
John C. Thies
Southern Services, Incorporated
Box
Birmingham, Alabama
810
Paul E. Thoman
General Services Administration - Region 3
7th & D Streets
Washington, D. C.
William K. Thomas
Thomas-Young Associates, Incorporated
525 Mill Street
Marion, Massachusetts
Donald H. Tingley
Tingley Engineering Company
314 West Lee Street
Charleston, West Virginia
Norio Tohda
Kajima Corporation
1-2-7, Moto-Akasaka, Minato-ku
Tokyo, Japan
J. M. Trews dale
University of Nottingham
Building Science Laboratory
Nottingham, England
Robert H. Tull
Private Consultant
Deer Hill Road, RD 3, Box 163
Lebanon, New Jersey
L. Bowman Turner
United McGi-1 Corporation
200 East Broadway
Westerville, Ohio
William E. Utt
U. S. Air Force
Washington, D. C.
E. N. Van Deventer
National Building Research Institute
P. 0. Box 395
Pretoria
Republic of South Africa
J. F. Van Straaten
National Building Research Institute
P. 0. Box 395
Pretoria
South Africa
Hari K. Varma
A Brompton Drive
Greensboro, North Carolina
(N. C. AT&T State University
Mechanical Engineering Department
Greensboro, North Carolina )
Tom A. Vernor , Jr.
P.E. Engineering Consultant
Central Power and Light Company
P. 0. Box
Corpus Christi, Texas
Iran Van Vi
Brace Research Institute of McGill University
MacDonald College
P. 0. Box 400
Ste. Anne De Bellevue
P. Quebec, Canada
J. C. Vorbeck
Charles J. R. McClure & Associates, Inc.
Old Olive Street Rd.
St. Louis, Missouri
Hiroshi WADA
Shinryo Air Conditioning Company, Ltd.
4, 2chome , Yotsuya
Shinjuku-ky
Tokyo , Japan
Milan W. Walker
National Institutes of Health
Rockville Pike
Bethesda, Maryland
Robert Walker (084)
Veterans Administration
810 Vermont Avenue, N.W.
Washington, D. C.
Dr. Gerald T. Ward
Brace Research Institute of McGill University
MacDonald College, P. 0. Box 400
Ste. Anne De Bellevue
P. Quebec, Canada
B. W. Ward, Jr.
Britt Alderman, Jr., Consulting Engineer
410 Bona Allen Building
Atlanta, Georgia
A. W. Ware
Abbott Laboratories
14th & Sheridan Road
North Chicago, Illinois
Jay Weening
T.S.W. International, Incorporated
Exchange Building
Memphis, Tennessee
W. T. White
General Services Administration
Building 41, Denver Federal Center
Denver, Colorado
John E. Williams
University of Michigan
School of Architecture
University of Michigan
Ann Arbor, Michigan
811
Thomas H. Williams
The Trane Company
Parklawn Drive
Rockville, Maryland
C. B. Wilson
Department of Architecture
University of Edinburgh
16-18 George Square
Edinburgh, Scotland
Foster C. Wilson
Owens-Corning Fiberglas Corporation
P. 0. Box 415, Technical Center
Granville, Ohio
J. J. Wisnewski
Perkins & Will Service Company, Inc.
Washington, D. C.
Donald R. Witt
Pennsylvania State University
Department of Architectural Engineering
101 Engineering "A"
University Park, Pennsylvania
L. D. Wood, Jr.
Sam R. Fogleman Associates
Consulting Engineers
Ponce De Leon Avenue
Rio Piedras, Puerto Rico 009 26
F. J. Wooldridge
W. Boyce Blanchard Consulting Engineer
355 Warrington Circle
Hampton, Virginia
M. J. Wooldridge
Commonwealth Scientific & Industrial
Research Organization
P. 0. Box 26
Highett, Victoria
Australia
Hitoshi Yamazaki
Kyusyu Institute of Design
226 Shiobara, Fukuoka, Japan
Koichi Yokoyama
Shin Nippon Air-Conditioning Co. , Ltd.
4-2, Hongoku-cho, Nihombaski
Chuo-ku, Tokyo
Japan
H. C. Yu
Hankins and Anderson, Consulting Engineers
North Hamilton Street
Richmond, Virginia
Dsvid J. Zabner
D. J. Zabner & Company
West McNichols Road
Detroit, Michigan
Willard R. Zahn
York Division, Borg-Warner Corporation
Richland Avenue
York, Pennsylvania
812
FORM NBS-1I4A 11-71) •
1 U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession
BIBLIOGRAPHIC DATA jjgg ggg 39 No.
3. Recipient's Accession No.
4. TITLE AND SUBTITLE
Use of Computers for Environmental Engineering Related to
Buildings, Proceedings of the First Symposium
5. Publication Date
'-'CHJUGIT J. 7 / J-
6. Performing Organization Code
7. AUTHOR(S)
8. Performing Organization
9. PERFORMING ORGANIZATION NAME AND ADDRESS
NATIONAL BUREAU OF STANDARDS
DEPARTMENT OF COMMERCE
10. Project/Task/Work Unit No.
11. Contract/Grant No,
12, Sponsoring Organization Name and Address
National Bureau of Standards, Washington, D. C.
American Society of Heating, Refrigerating and Air Conditioning
Engineers, Inc., United Engineering Center, New York, NY
Automated Procedures for Engineering Consultants, Inc., Dayton.
Ohio ' , y ,
13. Type of Report & Period
Covered
Final
14. Sponsoring Agency Code
15. SUPPLEMENTARY NOTES
16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant
bibliography or literature survey, mention it here.)
This proceedings of the First Symposium on the Use of Computers for Environmental
Engineering Related to Buildings contains all of the technical papers and invited
addresses presented at the symposium, which was held November 30 - December 2, ,
at the National Bureau of Standards.
The fifty-nine papers deal with the application of the computer to such environmental
engineering problems as building heat transfer calculations, heating and cooling load
calculations, system simulations, energy usage analyses, computer graphics, air and
smoke movement inside buildings, and weather data analyses for load and energy usage
calculations.
17. KEY WORDS (Alphabetical order, separated by semicolons)
Building heat transfer analysis, energy usage, environmental engineering, heating
and air conditioning, use of computers
18. AVAILABILITY STATEMENT
fxl UNLIMITED.
I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE
TO NTIS.
19. SECURITY CLASS
(THIS REPORT)
UNCLASSIFIED
20. SECURITY CLASS
(THIS PAGE)
UNCLASSIFIED
21. NO. OF PAGES
826
22. Price
$7. 75
USCOMM-DC -P71
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